Macro Reference

\[ \def\mathscr#1{\mathcal{#1}} \def\cbl#1{\mathopen{}\left\{#1\right.} \def\cbr#1{\mathopen{}\left.#1\right\}\mathclose{}} \def\cb#1{\mathopen{}\left\{#1\right\}\mathclose{}} \def\cbmat#1{\mathopen{}\left\{\begin{matrix}#1\end{matrix}\right\}\mathclose{}} \def\paren#1{\mathopen{}\left(#1\right)\mathclose{}} \def\pmat#1{\begin{pmatrix}#1\end{pmatrix}} \def\sparen#1{(#1)} \def\angb#1{\mathopen{}\left\langle #1\right\rangle\mathclose{}} \renewcommand{\sb}[1]{\mathopen{}\left[#1\right]\mathclose{}} \def\mathbbm#1{\mathbb{#1}} \def\distop#1{\mathbbm{#1}} \def\sbmat#1{\begin{bmatrix}#1\end{bmatrix}} \def\Prf#1{{\Pr\paren{#1}}} \def\Prunder#1#2{{\Pr_{#1}\paren{#2}}} \def\am{\arg \max} \def\argmax{\arg \max} \def\amin{\arg \min} \def\argmin{\arg \min} \def\p{\distop{p}} \def\f{\distop{f}} \def\F{\distop{F}} \def\h{\distop{h}} \def\H{\distop{H}} \def\pr{\p} \def\dens{\p} \def\pdens{\p} \def\fdens{\f} \def\mass{\P} \def\pmass{\P} \def\fmass{\F} \def\S{\distop{S}} \def\Sf#1{{\S\paren{#1}}} \def\surv{\distop{S}} \def\survf#1{{\surv\paren{#1}}} \def\survratio{\ratio_{\surv}} \def\rsurv{\survratio} \def\survr{\survratio} \def\survratiof#1{{\survratio\paren{#1}}} \def\rsurvf{\survratiof} \def\survrf{\survratiof} \def\riskset{\mathcal{R}} \def\risksetf#1{{\riskset\paren{#1}}} \def\Q{\distop{Q}} \def\quantile{\distop{Q}} \def\Qf#1{{\Q\paren{#1}}} \def\quantilef#1{{\quantile\paren{#1}}} \def\hQ{\mathop{\hat{\Q}}\nolimits} \def\hquantile{\mathop{\hat{\quantile}}\nolimits} \def\hQf#1{{\hQ\paren{#1}}} \def\hquantilef#1{{\hquantile\paren{#1}}} \def\ph{\mathop{\hat{\p}}\nolimits} \def\P{\mathbb{P}} \def\hp{\mathop{\hat{\p}}\nolimits} \def\ga{\alpha} \def\a{\alpha} \def\b{\beta} \def\g{\gamma} \def\floor#1{\mathopen{}\left\lfloor#1\right\rfloor\mathclose{}} \def\ceiling#1{\mathopen{}\left\lceil#1\right\rceil\mathclose{}} \def\ceil#1{{\ceiling{#1}}} \def\Ber{\operatorname{Ber}} \def\Bernoulli{\operatorname{Bernoulli}} \def\Pois{\operatorname{Pois}} \def\Poisson{\operatorname{Poisson}} \def\Gaus{\operatorname{Gaussian}} \def\Normal{\operatorname{N}} \def\ndist#1{{\Normal\paren{#1}}} \def\NB{\operatorname{NegBin}} \def\NegBin{\operatorname{NegBin}} \def\vbeta{\vec \beta} \def\vcoef{\vbeta} \def\regcoef{\beta} \def\Regcoef{B} \def\coef#1{\regcoef_{#1}} \def\Coef#1{\Regcoef_{#1}} \def\intcoef{\coef{0}} \def\Intcoef{\Coef{0}} \def\vb{\vec \beta} \def\vzero{\vec{0}} \def\vone{\vec{1}} \def\gb{\beta} \def\gg{\gamma} \def\gd{\delta} \def\eps{\varepsilon} \def\cdev{\popdev} \def\veps{\vec{\varepsilon}} \def\epsp#1{{\eps\paren{#1}}} \def\epsf{\epsp} \def\om{\omega} \def\m{\mu} \def\mean{\mu} \def\pmean{\mu} \def\popmean{\mu} \def\vm{\vec \m} \def\s{\sigma} \def\l{\lambda} \def\gl{\lambda} \def\lam{\lambda} \def\k{\kappa} \def\cs{\kappa} \def\condsurv{\kappa} \def\gs{\sigma} \def\gm{\mu} \def\M{M} \def\gM{M} \def\Mu{M} \def\cd{\cdot} \def\cds{\cdots} \def\lds{\ldots} \def\eqdef{\stackrel{\text{def}}{=}} \def\defeq{\stackrel{\text{def}}{=}} \def\eqby#1{\overset{#1}{=}} \def\hb{\hat \beta} \def\hcoef#1{\hat{\regcoef}_{#1}} \def\hintcoef{\hcoef{0}} \def\hvb{\hat{\vb}} \def\hvcoef{\hvb} \def\vhcoef{\hvb} \def\hR{\hat{R}} \def\hk{\hat \kappa} \def\hkappa{\hat \kappa} \def\hl{\hat \lambda} \def\hy{\hat y} \def\yh{\hat y} \def\fitted{\hy} \def\V{{\operatorname{Var}}} \def\hs{\hat \sigma} \def\hsig{\hat \sigma} \def\hS{\hat \Sigma} \def\hSig{\hat \Sigma} \def\hSigma{\hat \Sigma} \def\hsurv{\mathop{\hat{\surv}}\nolimits} \def\hSurv{\mathop{\hat{\surv}}\nolimits} \def\hSurvf#1{{\hSurv\paren{#1}}} \def\emp{\text{emp}} \def\km{\text{KM}} \def\naa{\text{NA}} \def\hsemp{\hsurv_{\emp}} \def\hskm{\hsurv_{\km}} \def\hsnaa{\hsurv_{\naa}} \def\hsempf#1{{\hsemp\paren{#1}}} \def\hskmf#1{{\hskm\paren{#1}}} \def\hsnaaf#1{{\hsnaa\paren{#1}}} \def\dist{\ \sim \ } \def\ddist{\ \dot{\sim} \ } \def\dsim{\ \dot{\sim} \ } \def\za{z_{1 - \frac{\alpha}{2}}} \def\ciradsym{\xi} \def\cirad{\za \cdot \hse{\hb}} \def\ciradf#1{\za \cdot \hse{#1}} \def\ci{\hb {\color{red}\pm} \cirad} \def\cilo{L} \def\ciup{U} \def\cilof#1{{\cilo\paren{#1}}} \def\ciupf#1{{\ciup\paren{#1}}} \def\cintf#1{{\sb{\cilof{#1}, \ciupf{#1}}}} \def\th{\theta} \def\vth{\vec{\theta}} \def\Th{\Theta} \def\smean#1{{\bar{#1}}} \def\xbar{\smean{x}} \def\samplemean#1#2{{\smean{#1}_{#2}}} \def\hth{\hat\theta} \def\hthml{\hth_{\text{ML}}} \def\ba{\begin{aligned}} \def\ea{\end{aligned}} \def\ind{\perp\!\!\!\perp} \def\indpt{\ind} \def\indold{⫫} \def\all{\forall} \def\iid{\operatorname{iid}} \def\ciid{\operatorname{ciid}} \def\simind{\ \sim_{\ind}\ } \def\siid{\ \sim_{\iid}\ } \def\sciid{\ \sim_{\ciid}\ } \def\simiid{\siid} \def\distiid{\siid} \def\tf{\therefore} \def\Lik{\mathcal{L}} \def\llik{\ell} \def\loss{L} \def\lossf#1{{\loss\paren{#1}}} \def\obsloss#1{\ell_{#1}} \def\poprisk{R} \def\popriskf#1{{\poprisk\paren{#1}}} \def\condpopriskf#1#2{{\poprisk\paren{#1 \mid #2}}} \def\modelfam{\mathcal{H}} \def\growthfn{m_{\predfam}} \def\growthfnf#1{{\growthfn\paren{#1}}} \def\vcdim{d_{\mathrm{VC}}} \def\vcdimf#1{{\vcdim\paren{#1}}} \def\failprob{\delta} \def\modmem{h} \def\modmemf#1{{\modmem\paren{#1}}} \def\modmemof#1{\modmem_{#1}} \def\nobs{n} \def\nmodels{M} \def\ninputvars{p} \def\inputdim{\ninputvars} \def\noutvars{q} \def\nparams{p^{*}} \def\nnetparams{P} \def\iter{t} \def\steplen{s} \def\iterpoint#1#2{{{#1}^{(#2)}}} \def\layeridx{\ell} \def\RSS{\operatorname{RSS}} \def\SSE{\operatorname{SSE}} \def\TSS{\operatorname{TSS}} \def\npatterns{K} \def\nreps{m} \def\nevents{s} \def\popdist{P} \def\targetfn{\mu} \def\targetfnf#1{{\targetfn\paren{#1}}} \def\truemeanfn{\mu} \def\truemeanfnf#1{{\truemeanfn\paren{#1}}} \def\truemean{\mu} \def\truemeanf#1{{\truemean\paren{#1}}} \def\truemeansubf#1#2{{\truemean_{#1}\paren{#2}}} \def\cmean{\truemean_{\Outvar \given \Predvar}} \def\cmeanf#1{\truemeansubf{\Outvar \given \Predvar}{#1}} \def\dataset{\mathcal{D}} \def\trainset{\mathcal{D}_{\text{train}}} \def\valset{\mathcal{D}_{\text{val}}} \def\testset{\mathcal{D}_{\text{test}}} \def\trainidx{I_{\text{train}}} \def\validx{I_{\text{val}}} \def\testidx{I_{\text{test}}} \def\bestmod{h^*} \def\bestmodf#1{{\bestmod\paren{#1}}} \def\avgfit{\popmean_{\modmem}} \def\avgfitf#1{{\avgfit\paren{#1}}} \def\hidval{h} \def\hidvalof#1{\hidval_{#1}} \def\vhidval{\vecf{\hidval}} \def\imgheight{h} \def\imgwidth{w} \def\poolsize{q} \def\hatmat{H} \def\leverage#1{h_{#1}} \def\avgleverage{\smean{h}} \def\cutheight{h} \def\clusterassign{C} \def\clusterassignf#1{{\clusterassign\paren{#1}}} \def\lpnorm#1{\ell_{#1}} \def\lbound{\ell} \def\ubound{u} \def\hf{\hat{f}} \def\hfx#1{{\hf\paren{#1}}} \def\loglik{\llik} \def\logl{\llik} \def\llikf#1{{\llik \paren{#1}}} \def\Likf#1{{\Lik\paren{#1}}} \def\loglikf{\llikf} \def\loglf{\llikf} \def\likf{\llikf} \def\deviance{\operatorname{dev}} \def\nulldeviance{\deviance_0} \def\satllik{\llik_{\mathrm{sat}}} \def\satdeviance{\deviance_{\mathrm{sat}}} \def\dicdev{\deviance_{\mathrm{DIC}}} \def\dicdevf#1{{\dicdev\paren{#1}}} \def\deviation{\devval} \def\devn{\deviation} \def\deviationv{\vec{\deviation}} \def\devnv{\deviationv} \def\deviationf#1#2{{\devsym_{#2}\paren{#1}}} \def\smeandev{\smean{\deviation}} \def\popdev{\deviation} \def\popdevf#1{\popdev_{#1}} \def\Deviation{\Delta} \def\Devn{\Deviation} \def\devof#1#2{{\paren{#1 - #2}}} \def\esterr#1#2{{\err_{#2}\paren{#1}}} \def\residual{\est{\Noise}} \def\resid{\residual} \def\Residual{\residual} \def\Resid{\Residual} \def\stdresidual{{\residual'{}}} \def\stdresid{\stdresidual} \def\StdResidual{\stdresidual} \def\StdResid{\StdResidual} \def\modresidual{{\residual^*{}}} \def\modresid{\modresidual} \def\ModResidual{\modresidual} \def\ModResid{\ModResidual} \def\prederr{{\varepsilon_{\text{pred}}}} \def\prederrf#1{{\prederr\paren{#1}}} \def\sqprederr{{\sqf{\prederr}}} \def\sqprederrf#1{{\sqf{\prederrf{#1}}}} \def\score{\llik'} \def\scorev{\vec{\llik'}} \def\scorei{\vec{\llik_i'}} \def\scorevi{\vec{\llik_i'}} \def\scoref#1{{\score \paren{#1}}} \def\hess{\llik''} \def\hessm{\llik''} \def\hessian{\hess} \def\hessij{\llik_{ij}''} \def\hessijalt{{\sb{\hess}}_{ij}} \def\hessf#1{{\hess \paren{#1}}} \def\hessianf{\hessf} \def\starf#1{#1^*} \def\lik{\llik} \def\est#1{\hat{#1}} \def\Est#1{\widehat{#1}} \def\esttmp#1{{\Est{#1}}^*} \def\esttmpl{\esttmp{\lambda}} \def\cR{\mathcal{R}} \def\range{\mathcal{R}} \def\Range{\mathcal{R}} \def\rangef#1{\cR(#1)} \def\modef#1{{\operatorname{mode}\paren{#1}}} \def\seq#1#2{#1{:}#2} \def\~{\approx} \def\dapp{\dot\approx} \def\deriv#1{\frac{\partial}{\partial #1}} \def\dderiv#1{\frac{\partial^2}{\partial #1^2}} \def\derivf#1#2{\frac{\partial #1}{\partial #2}} \def\derivff#1#2{\frac{\partial #2}{\partial #1}} \def\derivfnd{\derivf} \def\derivfdn{\derivff} \def\dderivf#1#2{\frac{\partial^2 #1}{\partial #2^2}} \def\xderiv#1#2{\frac{\partial^2}{\partial #1 \partial #2}} \def\xderivf#1#2#3{\frac{\partial^2 #1}{\partial #2 \partial #3}} \def\xderivff#1#2#3{\frac{\partial^2 #3}{\partial #1 \partial #2}} \def\derivfslash#1#2{{\partial #1 / \partial #2}} \def\grad{\nabla} \def\gradf#1{\grad #1} \def\gradwrt#1#2{\grad_{#1} #2} \def\dif#1#2{\frac{d #1}{d #2}} \def\red#1{{\color{red}{#1}}} \def\green#1{{\color{green}{#1}}} \def\blue#1{{\color{blue}{#1}}} \def\cyan#1{{\color{cyan}{#1}}} \def\magenta#1{{\color{magenta}{#1}}} \def\yellow#1{{\color{yellow}{#1}}} \def\black#1{{\color{black}{#1}}} \def\gray#1{{\color{gray}{#1}}} \def\white#1{{\color{white}{#1}}} \def\darkgray#1{{\color{darkgray}{#1}}} \def\lightgray#1{{\color{lightgray}{#1}}} \def\brown#1{{\color{brown}{#1}}} \def\lime#1{{\color{lime}{#1}}} \def\olive#1{{\color{olive}{#1}}} \def\orange#1{{\color{orange}{#1}}} \def\pink#1{{\color{pink}{#1}}} \def\purple#1{{\color{purple}{#1}}} \def\teal#1{{\color{teal}{#1}}} \def\violet#1{{\color{violet}{#1}}} \def\hE#1{{\mathop{\hat{\mathbb{E}}}\nolimits\sb{#1}}} \def\hExp{\hE} \def\hExpf{\hE} \def\hmu{\hat{\mu}} \def\hmuf#1{{\hmu\paren{#1}}} \def\Expp{\mathbb{E}} \def\Ep{\mathbb{E}} \def\expit{\operatorname{expit}} \def\expitf#1{{\expit\cb{#1}}} \def\dexpitf#1{{\expit'\cb{#1}}} \def\logit{\operatorname{logit}} \def\sigmoid{\expit} \def\sigmoidf#1{{\expit\paren{#1}}} \def\logitf#1{{\logit\cb{#1}}} \def\E#1{{\mathbb{E}\sb{#1}}} \def\Ef{\E} \def\Exp{\E} \def\Expf{\E} \def\Expfc#1#2{{\mathbb{E}_{#1}\sb{#2}}} \def\ATT{\operatorname{ATT}} \def\ATTf#1{{\ATT\paren{#1}}} \def\evalbar#1{\left.{#1}\right|} \def\evalAt#1#2{\evalbar{#1}_{#2}} \def\Varr{\operatorname{Var}} \def\Vart{\operatorname{Var}} \def\hvar{\mathop{\widehat{\Vart}}\nolimits} \def\hvart{\mathop{\widehat{\Vart}}\nolimits} \def\Covt{\operatorname{Cov}} \def\hcovt{\mathop{\widehat{\Covt}}\nolimits} \def\hCovt{\mathop{\widehat{\Covt}}\nolimits} \def\var#1{{\operatorname{Var}\paren{#1}}} \def\varf{\var} \def\Var{\var} \def\hVar#1{{\mathop{\widehat{\operatorname{Var}}}\nolimits\paren{#1}}} \def\Varf{\var} \def\hvarf#1{{\hvart\paren{#1}}} \def\Cov#1{{\Covt \paren{#1}}} \def\Covs#1#2{{\Covt \paren{#1, #2}}} \def\Covf{\Cov} \def\covh#1{{\hcovt\paren{#1}}} \def\covhf{\covh} \def\hcovf{\covh} \def\aVar#1{{\operatorname{aVar}\paren{#1}}} \def\aCov#1{{\operatorname{aCov}\paren{#1}}} \def\cum#1{{\operatorname{cum}\paren{#1}}} \def\Cort{\operatorname{Cor}} \def\hcort{\mathop{\widehat{\Cort}}\nolimits} \def\Cor#1{{\Cort \paren{#1}}} \def\Corf{\Cor} \def\Cors#1#2{{\Cort \paren{#1, #2}}} \def\hCor#1{{\hcort\paren{#1}}} \def\hCorf{\hCor} \def\hCors#1#2{{\hcort\paren{#1, #2}}} \def\med{\operatorname{med}} \def\medf#1{{\med\paren{#1}}} \def\IQR{\operatorname{IQR}} \def\IQRf#1{{\IQR\paren{#1}}} \def\varht{\mathop{\widehat{\operatorname{Var}}}\nolimits} \def\varh#1{{\varht\paren{#1}}} \def\varhf{\varh} \def\vc#1{\boldsymbol{#1}} \def\sd#1{{\operatorname{sd}\paren{#1}}} \def\SD#1{{\operatorname{SD}\paren{#1}}} \def\hSD#1{{\mathop{\widehat{\operatorname{SD}}}\nolimits\paren{#1}}} \def\hSDf{\hSD} \def\se#1{{\operatorname{se}\paren{#1}}} \def\hset{\mathop{\widehat{\operatorname{se}}}\nolimits} \def\hSE{\mathop{\widehat{\operatorname{SE}}}\nolimits} \def\hSEt{\mathop{\widehat{\operatorname{SE}}}\nolimits} \def\sef{\se} \def\hse#1{{\hset\paren{#1}}} \def\hsef{\hse} \def\SE#1{{\operatorname{SE}\paren{#1}}} \def\SEf{\SE} \def\SDf{\SD} \def\HSE#1{{\hSE\paren{#1}}} \def\hSEf{\HSE} \def\logt{\operatorname{log}} \def\logf#1{{\logt\cb{#1}}} \def\dlog{\logt'} \def\dlogf#1{{\dlog \cb{#1}}} \def\lnf#1{{\ln\paren{#1}}} \def\maxf#1{{\max\paren{#1}}} \def\minf#1{{\min\paren{#1}}} \def\sinf#1{{\sin\paren{#1}}} \def\cosf#1{{\cos\paren{#1}}} \def\tanhf#1{{\tanh\paren{#1}}} \def\detf#1{{\det\paren{#1}}} \renewcommand{\exp}[1]{{\operatorname{exp}\cb{#1}}} \def\expt{\operatorname{exp}} \def\expf#1{{\operatorname{exp}\cb{#1}}} \def\expfn{\expf} \def\dexp{\operatorname{exp}'} \def\dexpf#1{{\dexp \cb{#1}}} \def\euler{\text{e}} \def\e#1{\euler^{#1}} \def\ef{\e} \def\inv#1{{\paren{#1}}^{-1}} \def\invf{\inv} \def\invp{\inv} \def\invcb#1{{\cb{#1}}^{-1}} \def\invsb#1{{\sb{#1}}^{-1}} \def\oinf{I} \def\oinfm{\mat{I}} \def\Nat{\mathbb{N}} \def\oinff#1{{\oinf\paren{#1}}} \def\einf{\mathcal{I}} \def\EInf{\einf} \def\FInf{\einf} \def\einfm{\mathcal{I}} \def\einff#1{{\einf\paren{#1}}} \def\heinf{\hat{\einf}} \def\heinff#1{{\heinf \paren{#1}}} \def\1#1{\text{1}_{#1}} \def\indic#1{\mathbb{1}_{#1}} \def\indicp#1{{\mathbb{1}\paren{#1}}} \def\indiccb#1{{\mathbb{1}\cb{#1}}} \def\indicf{\indic} \def\set#1{{\cb{#1}}} \def\setbuild#1#2{{\set{#1 : #2}}} \def\setdiff#1#2{{#1 \setminus #2}} \def\pf#1{{\p \paren{#1}}} \def\Pf#1{{\P \paren{#1}}} \def\Bias#1{{\operatorname{Bias}\paren{#1}}} \def\bias{\Bias} \def\ss{\sigma^2} \def\ssqf#1{{\sigma^2\paren{#1}}} \def\mselr#1{{\operatorname{MSE}\paren{#1}}} \def\maelr#1{{\operatorname{MAE}\paren{#1}}} \def\abs#1{\mathopen{}\left|#1\right|\mathclose{}} \def\norm#1{\mathopen{}\left\lVert#1\right\rVert\mathclose{}} \def\normsq#1{{\norm{#1}}\sq} \def\normF#1{{{\norm{#1}}_{\mathrm{F}}}} \def\normFsq#1{{{\norm{#1}}_{\mathrm{F}}\sq}} \def\card#1{{\abs{#1}}} \def\powersetsym{\mathcal{P}} \def\powerset#1{{\powersetsym\paren{#1}}} \def\factorial#1{{{#1}!}} \def\binomial#1#2{{\binom{#1}{#2}}} \def\sumsym{s} \def\Sumsym{S} \def\sumof#1{{\sumsym_{#1}}} \def\Sumof#1{{\Sumsym_{#1}}} \def\powf#1#2{{\paren{#1}}^{#2}} \def\sqf#1{\powf{#1}{2}} \def\devsq#1#2{\sqf{\devsym_{#2}\paren{#1}}} \def\ssdev#1{\suminf{\devsq{\rvar_\iobs}{#1}}} \def\sq{^2} \def\err{\eps} \def\erf#1{{\err\paren{#1}}} \renewcommand{\vec}[1]{\vecf{#1}} \def\vecf#1{\mathord{\smash[b]{\underset{\raise.3ex\hbox{$\scriptstyle\sim$}}{#1}}\vphantom{#1}}} \renewcommand{\v}[1]{\vecf{#1}} \def\matr#1{\mathbf{#1}} \def\mX{\matr{X}} \def\mx{\matr{x}} \def\va{\vecf{a}} \def\vx{\vecf{x}} \def\vxs{\mathord{{\vec{x}^*}}} \def\diff{\Delta} \def\diffvx{\diff\vx} \def\vxi{\vecf{x}_i} \def\vX{\vecf{X}} \def\vy{\vecf{y}} \def\vY{\vecf{Y}} \def\outvar{y} \def\Outvar{Y} \def\signoutvar{\tilde{\outvar}} \def\voutvar{\vecf{\outvar}} \def\vOutvar{\vecf{\Outvar}} \def\eoutvar{\est{\outvar}} \def\veoutvar{\vecf{\eoutvar}} \def\predvar{x} \def\Predvar{X} \def\vpredvar{\vecf{\predvar}} \def\diffvpredvar{\diff\vpredvar} \def\vPredvar{\vecf{\Predvar}} \def\mpredvar{\matr{\Predvar}} \def\moutvar{\matr{\Outvar}} \def\mcoef{\matr{\Regcoef}} \def\mnoise{\matr{E}} \def\vresid{\vecf{\resid}} \def\vprederr{\vecf{\prederr}} \def\vz{\vecf{z}} \def\vZ{\vecf{Z}} \def\vD{\vecf{D}} \def\vd{\vecf{d}} \def\vT{\vecf{T}} \def\vt{\vecf{t}} \def\vpi{\vecf{\pi}} \def\vw{\vecf{w}} \def\vv{\vecf{v}} \def\vh{\vecf{h}} \def\ve{\vecf{e}} \def\vu{\vecf{u}} \def\vg{\vecf{g}} \def\vp{\vecf{p}} \def\vq{\vecf{q}} \def\vr{\vecf{r}} \def\vconst{\vecf{c}} \def\vdelta{\vecf{\delta}} \def\vepsilon{\vecf{\epsilon}} \def\vphi{\vecf{\phi}} \def\mat#1{\mathbf{#1}} \def\dsn#1{#1_1, \ldots, #1_n} \def\Xin{\dsn{X}} \def\xin{\dsn{x}} \def\yin{\dsn{y}} \def\'{^{\top}} \def\pt#1{{\paren{#1}}^{\top}} \def\tp#1{{#1}^{\top}} \def\dpr{\cdot} \def\Xxin{X_1=x_1, \ldots, X_n = x_n} \def\dprod#1#2{#1 \cdot #2} \def\dprodf{\dprod} \def\dpf{\dprodf} \def\tprod#1#2{\tp{#1} #2} \def\tprodf{\tprod} \def\ccprod#1#2{\tp{#1} #2} \def\ccp{\ccprod} \def\cpf{\ccprod} \def\iprod#1#2{{\angb{#1, #2}}} \def\iprodf{\iprod} \def\oprod#1#2{#1 \tp{#2}} \def\stprod#1{\ccprod{#1}{#1}} \def\gram{\stprod} \def\qform#1#2{\tp{#2} #1 #2} \def\siprod#1{\iprod{#1}{#1}} \def\soprod#1{#1 \tp{#1}} \def\sdprod#1{\dprod{#1}{#1}} \def\sdprodf{\sdprod} \def\cossim{\operatorname{cossim}} \def\cossimf#1#2{{\cossim\paren{#1, #2}}} \def\dsvn#1#2{#1_1=#2_1, \ldots, #1_n = #2_n} \def\sumn#1{\sum_{#1=1}^n} \def\sumnf#1#2{{\sumn{#1} \paren{#2}}} \def\sumto#1#2{\sum_{#1=1}^{#2}} \def\sumtof#1#2#3{{\sumto{#1}{#2} \paren{#3}}} \def\sumin{\sum_{i=1}^n} \def\suminf#1{{\sumin \paren{#1}}} \def\sumkK{\sum_{k=1}^{K}} \def\sumkKf#1{{\sumkK \paren{#1}}} \def\sumiN{\sum_{i=1}^N} \def\sumiNf#1{{\sumiN \paren{#1}}} \def\sumip{\sum_{i=1}^p} \def\sumipf#1{{\sumip \paren{#1}}} \def\sumjn{\sum_{j=1}^n} \def\sumjnf#1{{\sumjn \paren{#1}}} \def\sumjp{\sum_{j=1}^p} \def\sumjpf#1{{\sumjp \paren{#1}}} \def\prodin{\prod_{i=1}^n} \def\prodinf#1{{\prodin \paren{#1}}} \def\avgin{\frac{1}{n}\sumin} \def\avginf#1{{\avgin \paren{#1}}} \def\avgiN{\frac{1}{N}\sumiN} \def\avgiNf#1{{\avgiN \paren{#1}}} \def\avgto#1#2{\frac{1}{#2}\sumto{#1}{#2}} \def\avgtof#1#2#3{{\avgto{#1}{#2} \paren{#3}}} \def\avgon#1{\frac{1}{\abs{#1}}\sum_{\iobs \in #1}} \def\avgonf#1#2{{\avgon{#1} \paren{#2}}} \def\lp#1{\dprodf{#1}{\vb}} \def\lpdp{\lp{\vx}} \def\lincomp{\eta} \def\odds{\omega} \def\OR{\operatorname{OR}} \def\RD{\operatorname{RD}} \def\RR{\operatorname{RR}} \def\koppa{\text{ϙ}} \def\Koppa{\text{Ϙ}} \def\qoppa{\koppa} \def\Qoppa{\Koppa} \def\ratio{\koppa} \def\ratiof#1{{\ratio\paren{#1}}} \def\Ratio{\Koppa} \def\Ratiof#1{{\Ratio\paren{#1}}} \def\ror{\ratio_{\odds}} \def\orf#1{{\ror\paren{#1}}} \def\logodds{\lincomp} \def\logoddsf#1{{\logodds \paren{#1}}} \def\difflogodds{\diff \logodds} \def\hdifflogodds{\widehat{\difflogodds}} \def\diffeta{\diff \eta} \def\oddst{\operatorname{odds}} \def\probst{\operatorname{probs}} \def\probt{\operatorname{prob}} \def\riskt{\operatorname{risk}} \def\logoddst{\text{log-odds}} \def\prob{\pi} \def\probs{\pi} \def\risk{\pi} \def\prev{\pi} \def\potout#1{Y_{#1}} \def\potprob#1{\prob_{#1}} \def\potmean#1{\mean_{#1}} \def\obsprob#1{{\prob\paren{#1}}} \def\obsmean#1{{\mean\paren{#1}}} \def\py{\potout} \def\ppi{\potprob} \def\pmu{\potmean} \def\opi{\obsprob} \def\omu{\obsmean} \def\probit{\operatorname{probit}} \def\oddsf#1{{\oddst\cb{#1}}} \def\doddsf#1{{{\oddst}'\cb{#1}}} \def\oddsinv{\oddst^{-1}} \def\invodds{\operatorname{invodds}} \def\oddsinvf#1{{\oddsinv\cb{#1}}} \def\invoddsf#1{{\invodds\cb{#1}}} \def\doddsinvf#1{{{\oddsinv}'\cb{#1}}} \def\dinvoddsf#1{{{\invodds}'\cb{#1}}} \def\rate{{\lambda}} \def\lograte{\lincomp} \def\haz{{\lambda}} \def\hazratio{\ratio_{\haz}} \def\hr{\hazratio} \def\rhaz{\hazratio} \def\hazr{\hazratio} \def\hrf#1{{\hazratio\paren{#1}}} \def\rhazf{\hrf} \def\hazrf{\hrf} \def\rateratio{\ratio_{\rate}} \def\rater{\rateratio} \def\rrate{\rateratio} \def\rateratiof#1{{\rateratio\paren{#1}}} \def\raterf{\rateratiof} \def\rratef{\rateratiof} \def\riskratio{\ratio_{\risk}} \def\rrisk{\riskratio} \def\riskr{\riskratio} \def\riskratiof#1{{\riskratio\paren{#1}}} \def\rriskf{\riskratiof} \def\riskrf{\riskratiof} \def\prevratio{\ratio_{\prev}} \def\prr{\prevratio} \def\prevratiof#1{{\prevratio\paren{#1}}} \def\prrf{\prevratiof} \def\loghaz{\lincomp} \def\diffloghaz{\diff \loghaz} \def\cuhaz{{\Lambda}} \def\cumhaz{\cuhaz} \def\cuhazratio{\ratio_{\cuhaz}} \def\rcuhaz{\cuhazratio} \def\cuhazr{\cuhazratio} \def\cuhazratiof#1{{\cuhazratio\paren{#1}}} \def\rcuhazf{\cuhazratiof} \def\cuhazrf{\cuhazratiof} \def\factor{\theta} \def\factorf#1{{\factor\paren{#1}}} \def\oddsfactor{\factor_{\odds}} \def\oddsfactorf#1{{\oddsfactor\paren{#1}}} \def\fodds{\oddsfactor} \def\foddsf{\oddsfactorf} \def\hazfactor{\factor_{\haz}} \def\hazfactorf#1{{\hazfactor\paren{#1}}} \def\fhaz{\hazfactor} \def\fhazf{\hazfactorf} \def\ratefactor{\factor_{\rate}} \def\ratefactorf#1{{\ratefactor\paren{#1}}} \def\frate{\ratefactor} \def\fratef{\ratefactorf} \def\riskfactor{\factor_{\risk}} \def\riskfactorf#1{{\riskfactor\paren{#1}}} \def\frisk{\riskfactor} \def\friskf{\riskfactorf} \def\prevfactor{\factor_{\prev}} \def\prevfactorf#1{{\prevfactor\paren{#1}}} \def\fprev{\prevfactor} \def\fprevf{\prevfactorf} \def\cuhazfactor{\factor_{\cuhaz}} \def\cuhazfactorf#1{{\cuhazfactor\paren{#1}}} \def\fcuhaz{\cuhazfactor} \def\fcuhazf{\cuhazfactorf} \def\survfactor{\factor_{\surv}} \def\survfactorf#1{{\survfactor\paren{#1}}} \def\fsurv{\survfactor} \def\fsurvf{\survfactorf} \def\ff{\factorf} \def\oddsff{\oddsfactorf} \def\hazff{\hazfactorf} \def\rateff{\ratefactorf} \def\riskff{\riskfactorf} \def\prevff{\prevfactorf} \def\cuhazff{\cuhazfactorf} \def\survff{\survfactorf} \def\Surv{\surv} \def\incidence{\bar{\haz}} \def\phaz{\Expf{\haz}} \def\idmat{\mathbb{I}} \def\and{\cap} \def\reglincomb{\vx \cdot \vb} \def\regbetasum{\beta_1 x_1+ \dots + \beta_p x_p} \def\pdf{\distop{f}} \def\pmf#1{{\mathbb{P}\paren{#1}}} \def\cdf{\distop{F}} \def\cdff#1{{\cdf\paren{#1}}} \def\hcdf{\mathop{\hat{\cdf}}\nolimits} \def\hcdff#1{{\hcdf\paren{#1}}} \def\defLik{\Lik(\theta) \eqdef \p(\vX = \vx | \Theta = \theta)} \def\defLogLik{\lik \eqdef \logf{\Lik(\vx|\th)}} \def\defScore{\score \eqdef \deriv{\th} \lik(\vx|\th)} \def\defHess{\hess \eqdef \deriv{\vth}\deriv{\vth^{\top}} \llik(\vx | \vth)} \def\thmHessij{\hessij = \deriv{\th_i}\deriv{\th_j} \llik(\vX = \vx | \vth)} \def\defOInf{\oinf \eqdef -\hess(\vx|\vth)} \def\defEInf{\einf \eqdef \E{\oinf(\vx|\theta)}} \def\thmADistMLE{\hth_{ML}\ \dot \sim\ \ndist{\th,{\sb{\einf(\vth)}}^{-1}}} \def\eqGLMRatio{\ror(\vx,\vxs) = \exp{(\diffvx) \cdot \vb}} \def\defHR{\hr(t| \vx : \vxs) \eqdef \frac{\haz(t|\vx)}{\haz(t|\vxs)}} \def\kerngaus{\frac{-1}{2}\frac{(x-\mu)^2}{\ss}} \def\likgaus{{\paren{2\pi\ss}}^{-1/2}\expf{\kerngaus}} \def\llgaus{{\frac{-1}{2}\paren{\logf{2\pi\ss} + \frac{\devn^2}{\ss}}}} \def\scoreexpf{\frac{\devn}{\Varf{X}}} \def\llexpmean{-\logf{\pmean} - \frac{x}{\pmean}} \def\signt{\operatorname{sign}} \def\signf#1{{\signt\cb{#1}}} \def\reals{\mathbb{R}} \def\NA{\text{NA}} \def\resid{\residual} \def\stdresid{\stdresidual} \def\modresid{\modresidual} \def\ub{\underbrace} \def\ubf#1#2{\ub{#1}_{#2}} \def\dims#1#2{\ub{#1}_{#2}} \def\residv{\vecf{\residual}} \def\bbN{\mathbb{N}} \def\bbZ{\mathbb{Z}} \def\bbQ{\mathbb{Q}} \def\bbR{\mathbb{R}} \def\bbC{\mathbb{C}} \def\scrA{\mathscr{A}} \def\scrB{\mathscr{B}} \def\scrC{\mathscr{C}} \def\scrF{\mathscr{F}} \def\scrS{\mathscr{S}} \def\scrT{\mathscr{T}} \def\salg{\scrS} \def\salgS{\scrS} \def\salgT{\scrT} \def\sigmaalg{\salg} \def\sigmaalgebra{\salg} \def\borel{\scrB} \def\Borel{\borel} \def\borelalg{\borel} \def\events{\scrF} \def\eventspace{\events} \def\coll{\scrC} \def\collection{\coll} \def\gensalg#1{{\sigma\paren{#1}}} \def\gensigmaalg{\gensalg} \def\inas{\overset{\scriptstyle a.s.}{\longrightarrow}} \def\indist{\overset{\scriptstyle d}{\longrightarrow}} \def\inprob{\overset{\scriptstyle p}{\longrightarrow}} \def\plim{\operatorname{plim}} \def\plimf#1{{\plim\paren{#1}}} \def\tr{\operatorname{tr}} \def\trf#1{{\tr\paren{#1}}} \def\diag{\operatorname{diag}} \def\diagf#1{{\diag\paren{#1}}} \def\rank{\operatorname{rank}} \def\rankf#1{{\rank\paren{#1}}} \def\vct{\operatorname{vec}} \def\vctf#1{{\vct\paren{#1}}} \def\vcs{\operatorname{vecs}} \def\vcsf#1{{\vcs\paren{#1}}} \def\vch{\operatorname{vech}} \def\vchf#1{{\vch\paren{#1}}} \def\matvec{\vct} \def\matvecf{\vctf} \def\dBeta{\operatorname{Beta}} \def\dBetaf#1{{\dBeta\paren{#1}}} \def\dBern{\operatorname{Bern}} \def\dBernf#1{{\dBern\paren{#1}}} \def\dBin{\operatorname{Bin}} \def\dBinf#1{{\dBin\paren{#1}}} \def\dF{\operatorname{F}} \def\dFf#1{{\dF\paren{#1}}} \def\dGam{\operatorname{Gam}} \def\dGamf#1{{\dGam\paren{#1}}} \def\dInvGam{\operatorname{InvGam}} \def\dInvGamf#1{{\dInvGam\paren{#1}}} \def\dInvW{\operatorname{InvW}} \def\dInvWf#1{{\dInvW\paren{#1}}} \def\dLaplace{\operatorname{Laplace}} \def\dLaplacef#1{{\dLaplace\paren{#1}}} \def\dMN{\operatorname{MN}} \def\dMNf#1{{\dMN\paren{#1}}} \def\dN{\operatorname{N}} \def\dNf#1{{\dN\paren{#1}}} \def\dPo{\operatorname{Po}} \def\dPof#1{{\dPo\paren{#1}}} \def\dt{\operatorname{t}} \def\dtf#1{{\dt\paren{#1}}} \def\dW{\operatorname{W}} \def\dWf#1{{\dW\paren{#1}}} \def\dWeib{\operatorname{Weib}} \def\dWeibf#1{{\dWeib\paren{#1}}} \def\Ebar{\bar{\mathbb{E}}} \def\Ebarf#1{{\Ebar\sb{#1}}} \def\Ehat{\hat{\mathbb{E}}} \def\Ehatf#1{{\Ehat\sb{#1}}} \def\Etilde{\tilde{\mathbb{E}}} \def\Etildef#1{{\Etilde\sb{#1}}} \def\Corrt{\operatorname{Corr}} \def\Corr#1{{\Corrt\paren{#1}}} \def\Corrf{\Corr} \def\Corrs#1#2{{\Corrt\paren{#1, #2}}} \def\MSEt{\operatorname{MSE}} \def\MSE#1{{\MSEt\paren{#1}}} \def\MSEf{\MSE} \def\RMSEt{\operatorname{RMSE}} \def\RMSE#1{{\RMSEt\paren{#1}}} \def\RMSEf{\RMSE} \def\pMSEt{\operatorname{pMSE}} \def\pMSE#1{{\pMSEt\paren{#1}}} \def\pMSEf{\pMSE} \def\ESEt{\operatorname{ESE}} \def\ESE#1{{\ESEt\paren{#1}}} \def\ESEf{\ESE} \def\ESEEt{\operatorname{ESEE}} \def\ESEE#1{{\ESEEt\paren{#1}}} \def\ESEEf{\ESEE} \def\ESPEt{\operatorname{ESPE}} \def\ESPE#1{{\ESPEt\paren{#1}}} \def\ESPEf{\ESPE} \def\pRMSEt{\operatorname{pRMSE}} \def\pRMSE#1{{\pRMSEt\paren{#1}}} \def\pRMSEf{\pRMSE} \def\pMAEt{\operatorname{pMAE}} \def\pMAE#1{{\pMAEt\paren{#1}}} \def\pMAEf{\pMAE} \def\sMSEt{\operatorname{sMSE}} \def\sMSE#1{{\sMSEt\paren{#1}}} \def\sMSEf{\sMSE} \def\sRMSEt{\operatorname{sRMSE}} \def\sRMSE#1{{\sRMSEt\paren{#1}}} \def\sRMSEf{\sRMSE} \def\sMAEt{\operatorname{sMAE}} \def\sMAE#1{{\sMAEt\paren{#1}}} \def\sMAEf{\sMAE} \def\SEtildet{\widetilde{\operatorname{SE}}} \def\SEtilde#1{{\SEtildet\paren{#1}}} \def\SEtildef{\SEtilde} \def\Biast{\operatorname{Bias}} \def\biast{\operatorname{Bias}} \def\sign{\signt} \def\bfA{\mathbf{A}} \def\bfB{\mathbf{B}} \def\bfC{\mathbf{C}} \def\bfD{\mathbf{D}} \def\bfE{\mathbf{E}} \def\bfF{\mathbf{F}} \def\bfG{\mathbf{G}} \def\bfH{\mathbf{H}} \def\bfI{\mathbf{I}} \def\bfJ{\mathbf{J}} \def\bfK{\mathbf{K}} \def\bfL{\mathbf{L}} \def\bfM{\mathbf{M}} \def\bfN{\mathbf{N}} \def\bfO{\mathbf{O}} \def\bfP{\mathbf{P}} \def\bfQ{\mathbf{Q}} \def\bfR{\mathbf{R}} \def\bfS{\mathbf{S}} \def\bfT{\mathbf{T}} \def\bfU{\mathbf{U}} \def\bfV{\mathbf{V}} \def\bfW{\mathbf{W}} \def\bfX{\mathbf{X}} \def\bfY{\mathbf{Y}} \def\bfZ{\mathbf{Z}} \def\bfa{\mathbf{a}} \def\bfb{\mathbf{b}} \def\bfc{\mathbf{c}} \def\bfd{\mathbf{d}} \def\bfe{\mathbf{e}} \def\bff{\mathbf{f}} \def\bfg{\mathbf{g}} \def\bfh{\mathbf{h}} \def\bfi{\mathbf{i}} \def\bfj{\mathbf{j}} \def\bfk{\mathbf{k}} \def\bfl{\mathbf{l}} \def\bfm{\mathbf{m}} \def\bfn{\mathbf{n}} \def\bfo{\mathbf{o}} \def\bfp{\mathbf{p}} \def\bfq{\mathbf{q}} \def\bfr{\mathbf{r}} \def\bfs{\mathbf{s}} \def\bft{\mathbf{t}} \def\bfu{\mathbf{u}} \def\bfv{\mathbf{v}} \def\bfw{\mathbf{w}} \def\bfx{\mathbf{x}} \def\bfy{\mathbf{y}} \def\bfz{\mathbf{z}} \def\bfalpha{\boldsymbol{\alpha}} \def\bfbeta{\boldsymbol{\beta}} \def\bfdelta{\boldsymbol{\delta}} \def\bfepsilon{\boldsymbol{\epsilon}} \def\bfvarepsilon{\boldsymbol{\varepsilon}} \def\bfzeta{\boldsymbol{\zeta}} \def\bfeta{\boldsymbol{\eta}} \def\bftheta{\boldsymbol{\theta}} \def\bfvartheta{\boldsymbol{\vartheta}} \def\bfgamma{\boldsymbol{\gamma}} \def\bfkappa{\boldsymbol{\kappa}} \def\bflambda{\boldsymbol{\lambda}} \def\bfmu{\boldsymbol{\mu}} \def\bfnu{\boldsymbol{\nu}} \def\bfxi{\boldsymbol{\xi}} \def\bfpi{\boldsymbol{\pi}} \def\bfvarpi{\boldsymbol{\varpi}} \def\bfrho{\boldsymbol{\rho}} \def\bfvarrho{\boldsymbol{\varrho}} \def\bfsigma{\boldsymbol{\sigma}} \def\bfvarsigma{\boldsymbol{\varsigma}} \def\bftau{\boldsymbol{\tau}} \def\bfupsilon{\boldsymbol{\upsilon}} \def\bfphi{\boldsymbol{\phi}} \def\bfvarphi{\boldsymbol{\varphi}} \def\bfchi{\boldsymbol{\chi}} \def\bfpsi{\boldsymbol{\psi}} \def\bfomega{\boldsymbol{\omega}} \def\bfiota{\boldsymbol{\iota}} \def\bfGamma{\boldsymbol{\Gamma}} \def\bfDelta{\boldsymbol{\Delta}} \def\bfTheta{\boldsymbol{\Theta}} \def\bfLambda{\boldsymbol{\Lambda}} \def\bfXi{\boldsymbol{\Xi}} \def\bfPi{\boldsymbol{\Pi}} \def\bfSigma{\boldsymbol{\Sigma}} \def\bfUpsilon{\boldsymbol{\Upsilon}} \def\bfPhi{\boldsymbol{\Phi}} \def\bfPsi{\boldsymbol{\Psi}} \def\bfOmega{\boldsymbol{\Omega}} \def\bfzero{\boldsymbol{0}} \def\hprob{\hat{\prob}} \def\hprobs{\hprob} \def\hPr#1{{\mathop{\widehat{\Pr}}\nolimits\sb{#1}}} \def\hrisk{\hprob} \def\hprev{\hprob} \def\hpoprisk{\hat{\poprisk}} \def\hpopriskf#1{{\hpoprisk\paren{#1}}} \def\hmodmem{\hat{\modmem}} \def\hmodmemf#1{{\hmodmem\paren{#1}}} \def\hmodmemof#1{\hmodmem_{#1}} \def\htargetfn{\hat{\targetfn}} \def\htargetfnf#1{{\htargetfn\paren{#1}}} \def\hodds{\hat{\odds}} \def\hATT{\widehat{\ATT}} \def\hATTf#1{{\hATT\paren{#1}}} \def\hrate{\hat{\rate}} \def\hhaz{\hrate} \def\hcuhaz{\hat{\cuhaz}} \def\hcumhaz{\hcuhaz} \def\hkoppa{\hat{\koppa}} \def\hKoppa{\hat{\Koppa}} \def\hqoppa{\hkoppa} \def\hQoppa{\hKoppa} \def\hratio{\hat{\ratio}} \def\hratiof#1{{\hratio\paren{#1}}} \def\hRatio{\hat{\Ratio}} \def\hRatiof#1{{\hRatio\paren{#1}}} \def\hror{\hratio_{\odds}} \def\horf#1{{\hror\paren{#1}}} \def\hhazratio{\hratio_{\haz}} \def\hhr{\hhazratio} \def\hrhaz{\hhazratio} \def\hhazr{\hhazratio} \def\hhrf#1{{\hhazratio\paren{#1}}} \def\hrhazf{\hhrf} \def\hhazrf{\hhrf} \def\hrateratio{\hratio_{\rate}} \def\hrater{\hrateratio} \def\hrrate{\hrateratio} \def\hrateratiof#1{{\hrateratio\paren{#1}}} \def\hraterf{\hrateratiof} \def\hrratef{\hrateratiof} \def\hriskratio{\hratio_{\risk}} \def\hrrisk{\hriskratio} \def\hriskr{\hriskratio} \def\hriskratiof#1{{\hriskratio\paren{#1}}} \def\hrriskf{\hriskratiof} \def\hriskrf{\hriskratiof} \def\hRD{\widehat{\RD}} \def\hRR{\widehat{\RR}} \def\hprevratio{\hratio_{\prev}} \def\hprr{\hprevratio} \def\hprevratiof#1{{\hprevratio\paren{#1}}} \def\hprrf{\hprevratiof} \def\hsurvratio{\hratio_{\surv}} \def\hrsurv{\hsurvratio} \def\hsurvr{\hsurvratio} \def\hsurvratiof#1{{\hsurvratio\paren{#1}}} \def\hrsurvf{\hsurvratiof} \def\hsurvrf{\hsurvratiof} \def\hcuhazratio{\hratio_{\cuhaz}} \def\hrcuhaz{\hcuhazratio} \def\hcuhazr{\hcuhazratio} \def\hcuhazratiof#1{{\hcuhazratio\paren{#1}}} \def\hrcuhazf{\hcuhazratiof} \def\hcuhazrf{\hcuhazratiof} \def\hfactor{\hat{\factor}} \def\hfactorf#1{{\hfactor\paren{#1}}} \def\hff{\hfactorf} \def\hoddsfactor{\hfactor_{\odds}} \def\hoddsfactorf#1{{\hoddsfactor\paren{#1}}} \def\hfodds{\hoddsfactor} \def\hfoddsf{\hoddsfactorf} \def\hoddsff{\hoddsfactorf} \def\hhazfactor{\hfactor_{\haz}} \def\hhazfactorf#1{{\hhazfactor\paren{#1}}} \def\hfhaz{\hhazfactor} \def\hfhazf{\hhazfactorf} \def\hhazff{\hhazfactorf} \def\hratefactor{\hfactor_{\rate}} \def\hratefactorf#1{{\hratefactor\paren{#1}}} \def\hfrate{\hratefactor} \def\hfratef{\hratefactorf} \def\hrateff{\hratefactorf} \def\hriskfactor{\hfactor_{\risk}} \def\hriskfactorf#1{{\hriskfactor\paren{#1}}} \def\hfrisk{\hriskfactor} \def\hfriskf{\hriskfactorf} \def\hriskff{\hriskfactorf} \def\hprevfactor{\hfactor_{\prev}} \def\hprevfactorf#1{{\hprevfactor\paren{#1}}} \def\hfprev{\hprevfactor} \def\hfprevf{\hprevfactorf} \def\hprevff{\hprevfactorf} \def\hcuhazfactor{\hfactor_{\cuhaz}} \def\hcuhazfactorf#1{{\hcuhazfactor\paren{#1}}} \def\hfcuhaz{\hcuhazfactor} \def\hfcuhazf{\hcuhazfactorf} \def\hcuhazff{\hcuhazfactorf} \def\hsurvfactor{\hfactor_{\surv}} \def\hsurvfactorf#1{{\hsurvfactor\paren{#1}}} \def\hfsurv{\hsurvfactor} \def\hfsurvf{\hsurvfactorf} \def\hsurvff{\hsurvfactorf} \def\hCorrt{\mathop{\widehat{\Corrt}}\nolimits} \def\hCorr#1{{\hCorrt\paren{#1}}} \def\hCorrf{\hCorr} \def\hCorrs#1#2{{\hCorrt\paren{#1, #2}}} \def\hMSEt{\mathop{\widehat{\MSEt}}\nolimits} \def\hMSE#1{{\hMSEt\paren{#1}}} \def\hMSEf{\hMSE} \def\hRMSEt{\mathop{\widehat{\RMSEt}}\nolimits} \def\hRMSE#1{{\hRMSEt\paren{#1}}} \def\hRMSEf{\hRMSE} \def\hBiast{\mathop{\widehat{\Biast}}\nolimits} \def\hBias#1{{\hBiast\paren{#1}}} \def\hbias{\hBias} \def\eQ{\mathop{\est{\Q}}\nolimits} \def\equantile{\mathop{\est{\quantile}}\nolimits} \def\eQf#1{{\eQ\paren{#1}}} \def\equantilef#1{{\equantile\paren{#1}}} \def\ep{\mathop{\est{\p}}\nolimits} \def\eb{\est{\beta}} \def\ecoef#1{\est{\regcoef}_{#1}} \def\eintcoef{\ecoef{0}} \def\evb{\est{\vb}} \def\evcoef{\evb} \def\evhcoef{\evb} \def\eR{\est{R}} \def\ek{\est{\kappa}} \def\ekappa{\est{\kappa}} \def\el{\est{\lambda}} \def\ey{\est{y}} \def\efitted{\ey} \def\es{\est{\sigma}} \def\esig{\est{\sigma}} \def\eS{\est{\Sigma}} \def\eSig{\est{\Sigma}} \def\eSigma{\est{\Sigma}} \def\esurv{\mathop{\est{\surv}}\nolimits} \def\eSurv{\mathop{\est{\surv}}\nolimits} \def\eSurvf#1{{\eSurv\paren{#1}}} \def\esemp{\esurv_{\emp}} \def\eskm{\esurv_{\km}} \def\esnaa{\esurv_{\naa}} \def\esempf#1{{\esemp\paren{#1}}} \def\eskmf#1{{\eskm\paren{#1}}} \def\esnaaf#1{{\esnaa\paren{#1}}} \def\eth{\est{\theta}} \def\ethml{\eth_{\text{ML}}} \def\eE#1{{\mathop{\est{\mathbb{E}}}\nolimits\sb{#1}}} \def\eExp{\eE} \def\eExpf{\eE} \def\emu{\est{\mu}} \def\emuf#1{{\emu\paren{#1}}} \def\evar{\mathop{\Est{\Vart}}\nolimits} \def\evart{\mathop{\Est{\Vart}}\nolimits} \def\ecovt{\mathop{\Est{\Covt}}\nolimits} \def\eCovt{\mathop{\Est{\Covt}}\nolimits} \def\eVar#1{{\mathop{\Est{\operatorname{Var}}}\nolimits\paren{#1}}} \def\evarf#1{{\evart\paren{#1}}} \def\ecovf#1{{\ecovt\paren{#1}}} \def\ecort{\mathop{\Est{\Cort}}\nolimits} \def\eCor#1{{\ecort\paren{#1}}} \def\eCorf{\eCor} \def\eCors#1#2{{\ecort\paren{#1, #2}}} \def\eSD#1{{\mathop{\Est{\operatorname{SD}}}\nolimits\paren{#1}}} \def\eSDf{\eSD} \def\eset{\mathop{\Est{\operatorname{se}}}\nolimits} \def\eSE{\mathop{\Est{\operatorname{SE}}}\nolimits} \def\eSEt{\mathop{\Est{\operatorname{SE}}}\nolimits} \def\ese#1{{\eset\paren{#1}}} \def\esef{\ese} \def\eSEf#1{{\eSE\paren{#1}}} \def\eeinf{\est{\einf}} \def\eeinff#1{{\eeinf \paren{#1}}} \def\edifflogodds{\Est{\difflogodds}} \def\ecdf{\mathop{\est{\cdf}}\nolimits} \def\ecdff#1{{\ecdf\paren{#1}}} \def\eclassprior{\est{\pi}} \def\eprob{\est{\prob}} \def\eprobs{\eprob} \def\ePr#1{{\mathop{\Est{\Pr}}\nolimits\sb{#1}}} \def\erisk{\eprob} \def\eprev{\eprob} \def\epoprisk{\est{\poprisk}} \def\epopriskf#1{{\epoprisk\paren{#1}}} \def\emodmem{\est{\modmem}} \def\emodmemf#1{{\emodmem\paren{#1}}} \def\emodmemof#1{\emodmem_{#1}} \def\emodmemat#1{\emodmem_{#1}} \def\emodmematf#1#2{{\emodmemat{#1}\paren{#2}}} \def\etargetfn{\est{\targetfn}} \def\etargetfnf#1{{\etargetfn\paren{#1}}} \def\targeterr{\devsym_{\targetfn}} \def\targeterrf#1{{\targeterr\paren{#1}}} \def\emprisk{\epoprisk} \def\empriskf{\epopriskf} \def\eodds{\est{\odds}} \def\eATT{\Est{\ATT}} \def\eATTf#1{{\eATT\paren{#1}}} \def\erate{\est{\rate}} \def\ehaz{\erate} \def\ecuhaz{\est{\cuhaz}} \def\ecumhaz{\ecuhaz} \def\ekoppa{\est{\koppa}} \def\eKoppa{\est{\Koppa}} \def\eqoppa{\ekoppa} \def\eQoppa{\eKoppa} \def\eratio{\est{\ratio}} \def\eratiof#1{{\eratio\paren{#1}}} \def\eRatio{\est{\Ratio}} \def\eRatiof#1{{\eRatio\paren{#1}}} \def\eror{\eratio_{\odds}} \def\eorf#1{{\eror\paren{#1}}} \def\ehazratio{\eratio_{\haz}} \def\ehr{\ehazratio} \def\erhaz{\ehazratio} \def\ehazr{\ehazratio} \def\ehrf#1{{\ehazratio\paren{#1}}} \def\erhazf{\ehrf} \def\ehazrf{\ehrf} \def\erateratio{\eratio_{\rate}} \def\erater{\erateratio} \def\errate{\erateratio} \def\erateratiof#1{{\erateratio\paren{#1}}} \def\eraterf{\erateratiof} \def\erratef{\erateratiof} \def\eriskratio{\eratio_{\risk}} \def\errisk{\eriskratio} \def\eriskr{\eriskratio} \def\eriskratiof#1{{\eriskratio\paren{#1}}} \def\erriskf{\eriskratiof} \def\eriskrf{\eriskratiof} \def\eRD{\Est{\RD}} \def\eRR{\Est{\RR}} \def\eprevratio{\eratio_{\prev}} \def\eprr{\eprevratio} \def\eprevratiof#1{{\eprevratio\paren{#1}}} \def\eprrf{\eprevratiof} \def\esurvratio{\eratio_{\surv}} \def\ersurv{\esurvratio} \def\esurvr{\esurvratio} \def\esurvratiof#1{{\esurvratio\paren{#1}}} \def\ersurvf{\esurvratiof} \def\esurvrf{\esurvratiof} \def\ecuhazratio{\eratio_{\cuhaz}} \def\ercuhaz{\ecuhazratio} \def\ecuhazr{\ecuhazratio} \def\ecuhazratiof#1{{\ecuhazratio\paren{#1}}} \def\ercuhazf{\ecuhazratiof} \def\ecuhazrf{\ecuhazratiof} \def\efactor{\est{\factor}} \def\efactorf#1{{\efactor\paren{#1}}} \def\eff{\efactorf} \def\eoddsfactor{\efactor_{\odds}} \def\eoddsfactorf#1{{\eoddsfactor\paren{#1}}} \def\efodds{\eoddsfactor} \def\efoddsf{\eoddsfactorf} \def\eoddsff{\eoddsfactorf} \def\ehazfactor{\efactor_{\haz}} \def\ehazfactorf#1{{\ehazfactor\paren{#1}}} \def\efhaz{\ehazfactor} \def\efhazf{\ehazfactorf} \def\ehazff{\ehazfactorf} \def\eratefactor{\efactor_{\rate}} \def\eratefactorf#1{{\eratefactor\paren{#1}}} \def\efrate{\eratefactor} \def\efratef{\eratefactorf} \def\erateff{\eratefactorf} \def\eriskfactor{\efactor_{\risk}} \def\eriskfactorf#1{{\eriskfactor\paren{#1}}} \def\efrisk{\eriskfactor} \def\efriskf{\eriskfactorf} \def\eriskff{\eriskfactorf} \def\eprevfactor{\efactor_{\prev}} \def\eprevfactorf#1{{\eprevfactor\paren{#1}}} \def\efprev{\eprevfactor} \def\efprevf{\eprevfactorf} \def\eprevff{\eprevfactorf} \def\ecuhazfactor{\efactor_{\cuhaz}} \def\ecuhazfactorf#1{{\ecuhazfactor\paren{#1}}} \def\efcuhaz{\ecuhazfactor} \def\efcuhazf{\ecuhazfactorf} \def\ecuhazff{\ecuhazfactorf} \def\esurvfactor{\efactor_{\surv}} \def\esurvfactorf#1{{\esurvfactor\paren{#1}}} \def\efsurv{\esurvfactor} \def\efsurvf{\esurvfactorf} \def\esurvff{\esurvfactorf} \def\eCorrt{\mathop{\Est{\Corrt}}\nolimits} \def\eCorr#1{{\eCorrt\paren{#1}}} \def\eCorrf{\eCorr} \def\eCorrs#1#2{{\eCorrt\paren{#1, #2}}} \def\eMSEt{\mathop{\Est{\MSEt}}\nolimits} \def\eMSE#1{{\eMSEt\paren{#1}}} \def\eMSEf{\eMSE} \def\eRMSEt{\mathop{\Est{\RMSEt}}\nolimits} \def\eRMSE#1{{\eRMSEt\paren{#1}}} \def\eRMSEf{\eRMSE} \def\eBiast{\mathop{\Est{\Biast}}\nolimits} \def\eBias#1{{\eBiast\paren{#1}}} \def\ebias{\eBias} \def\sdpar{\sigma} \def\varpar{\sigma^2} \def\hsdpar{\hat{\sigma}} \def\esdpar{\est{\sdpar}} \def\hvarpar{\hat{\sigma}^2} \def\evarpar{\est{\sdpar}^2} \def\covmat{\Sigma} \def\hcovmat{\hat{\Sigma}} \def\ecovmat{\est{\covmat}} \def\corpar{\rho} \def\noise{\varepsilon} \def\Noise{\varepsilon} \def\vnoise{\vecf{\noise}} \def\vNoise{\vecf{\Noise}} \def\biassym{\mathbb{B}} \def\biassymf#1{{\biassym\sb{#1}}} \def\varsym{\mathbb{V}} \def\varsymf#1{{\varsym\sb{#1}}} \def\devsym{\mathbb{D}} \def\devsymf#1{{\devsym\sb{#1}}} \def\devval{\mathbbm{d}} \def\resvar{\varpar} \def\irrerr{\resvar} \def\rvar{x} \def\Rvar{X} \def\predbar{\smean{\predvar}} \def\outbar{\smean{\outvar}} \def\rvarbar{\smean{\rvar}} \def\sspred{S_{\predvar\predvar}} \def\ssout{S_{\outvar\outvar}} \def\sspredout{S_{\predvar\outvar}} \def\learnrate{\alpha} \def\regpar{\lambda} \def\eigval{\lambda} \def\Eigvals{\Lambda} \def\eigvalmax{{\eigval_{\max}}} \def\eigvalmin{{\eigval_{\min}}} \def\eigvalmaxf#1{{\eigvalmax\paren{#1}}} \def\eigvalminf#1{{\eigvalmin\paren{#1}}} \def\mdesign{\matr{D}} \def\design{\mdesign} \def\vdesign{\vecf{D}} \def\featmap{D} \def\vfeatmap{\vdesign} \def\normpdf{\phi} \def\normcdf{\Phi} \def\backerr{\delta} \def\vbackerr{\vecf{\delta}} \def\mbackerr{\Delta} \def\vhidgrad{\vecf{\epsilon}} \def\stepvec{\vecf{\delta}} \def\step{\delta} \def\quadmodel{q} \def\quadmodelf#1{{\quadmodel\paren{#1}}} \def\lingrad{{\vg_{\quadmodel}}} \def\lingradf#1{{\lingrad\paren{#1}}} \def\tolout{\varepsilon} \def\tolin{\delta} \def\smallconst{\varepsilon} \def\machineps{\varepsilon} \def\kron{\delta} \def\slack{\xi} \def\dualvar{\alpha} \def\lagmult{\lambda} \def\vlagmult{\vecf{\lambda}} \def\siglevel{\alpha} \def\thresh{\theta} \def\param{\theta} \def\vparam{\vec{\theta}} \def\hparam{\hat{\theta}} \def\eparam{\est{\param}} \def\hvparam{\hat{\vec{\theta}}} \def\evparam{\est{\vparam}} \def\Param{\Theta} \def\Paramspace{\Theta} \def\angpar{\theta} \def\shape{\alpha} \def\shapeb{\beta} \def\df{\operatorname{df}} \def\hdf{\hat{\operatorname{df}}} \def\edf{\est{\df}} \def\gammafn{\Gamma} \def\samplespace{\Omega} \def\outcome{\omega} \def\measure{\mu} \def\measureb{\nu} \def\lebesgue{\lambda} \def\condnum{\kappa} \def\change{\Delta} \def\vprob{\vecf{\pi}} \def\hmean{\hat{\mu}} \def\emean{\est{\mean}} \def\hregcoef{\hat{\beta}} \def\eregcoef{\est{\regcoef}} \def\armijo{c_1} \def\schedfrac{\zeta} \def\schedlen{\tau} \def\decay{\gamma} \def\clipthresh{\tau} \def\convrate{\rho} \def\coordfactor{\mu} \def\leak{\alpha} \def\linefn{\phi} \def\bandwidth{\sigma} \def\attnweight{\alpha} \def\degmat{\Delta} \def\penaltygrid{\Lambda} \def\prevalence{\pi} \def\recallweight{\beta} \def\resp{\gamma} \def\shrinkage{\nu} \def\singval{\sigma} \def\svfrac{\nu} \def\truthind{\delta} \def\truthindf#1{{\truthind\paren{#1}}} \def\typetwoerr{\beta} \def\unitthresh{\Theta} \def\votewt{\alpha} \def\wterr{\varepsilon} \def\strongconv{\mu} \def\combwt{\alpha} \def\combwtb{\beta} \def\errcov{\Omega} \def\midpt{\tau} \def\nullity{\nu} \def\lsresid{\varepsilon} \def\vlsresid{\vec{\varepsilon}} \def\subdiv{\Delta} \def\universe{\Omega} \def\lowend{\alpha} \def\highend{\beta} \def\precision{\tau} \def\hprecision{\hat{\tau}} \def\eprecision{\est{\precision}} \def\mahal{\Delta} \def\mahaldist{\delta} \def\rvrate{\Lambda} \def\overdisp{\rho} \def\adjlevel{\alpha} \def\foldassign{\kappa} \def\accept{\alpha} \def\estimand{\Delta} \def\stationary{\pi} \def\sdbetween{\tau} \def\event{\delta} \def\propstep{\varepsilon} \def\sdprior{\tau} \def\poismean{\phi} \def\sdest{\tau} \def\lrstat{\Lambda} \def\stat{T} \def\statf#1{{\stat\paren{#1}}} \def\sfac{g} \def\sfacf#1#2{{\sfac\paren{#1 ; #2}}} \def\rfac{h} \def\rfacf#1{{\rfac\paren{#1}}} \def\natparam{\eta} \def\vnatparam{\vecf{\natparam}} \def\basemeasure{\rfac} \def\basemeasuref#1{{\rfacf{#1}}} \def\logpartition{A} \def\logpartitionf#1{{\logpartition\paren{#1}}} \def\nuisance{\lambda} \def\hnuisance{\hat{\lambda}} \def\enuisance{\est{\nuisance}} \def\interest{\psi} \def\quantlevel{\beta} \def\tuning{\lambda} \def\hist#1#2{\bar{#1}_{#2}} \def\trthist#1{\hist{A}{#1}} \def\trtvalhist#1{\hist{a}{#1}} \def\covhist#1{\hist{L}{#1}} \def\covvalhist#1{\hist{l}{#1}} \def\censhist#1{\hist{C}{#1}} \def\censvalhist#1{\hist{c}{#1}} \def\eventnocens#1{D^{\bar{c}=0}_{#1}} \def\codealph{\Sigma} \def\srcalph{\mathcal{X}} \def\ffield#1{\mathbb{F}_{#1}} \def\hamdist#1#2{{\Delta\paren{#1, #2}}} \def\errfrac{\delta} \def\codeparams#1#2#3#4{{\sb{#1, #2, #3}}_{#4}} \def\bigO#1{{O\paren{#1}}} \def\littleo#1{{o\paren{#1}}} \def\asymub#1{{O\paren{#1}}} \def\entropy{\distop{H}} \def\entropyf#1{{\entropy\paren{#1}}} \def\surprisal{\distop{s}} \def\surprisalf#1{{\surprisal\paren{#1}}} \def\surprisalunderf#1#2{{\surprisal_{#1}\paren{#2}}} \def\rarity{\distop{r}} \def\rarityf#1{{\rarity\paren{#1}}} \def\rarityunderf#1#2{{\rarity_{#1}\paren{#2}}} \def\codelen{\ell} \def\codelenf#1{{\codelen\paren{#1}}} \def\expcodelen{L} \def\cprob#1{{{#1}^{\mathsf{c}}}} \def\perplexity{\mathrm{PP}} \def\perplexityf#1{{\perplexity\paren{#1}}} \def\crossentropy{\entropy} \def\crossentropyf#1#2{{\crossentropy\paren{#1, #2}}} \def\avgcrossent{\smean{\crossentropy}} \def\avgcrossentbase#1{{\avgcrossent_{#1}}} \def\kldiv{{D_{\mathrm{KL}}}} \def\kldivf#1#2{{\kldiv\paren{#1 \,\Vert\, #2}}} \def\mutinfo{\distop{I}} \def\mutinfof#1#2{{\mutinfo\paren{#1 ; #2}}} \def\cmutinfof#1#2#3{{\mutinfo\paren{#1 ; #2 \mid #3}}} \def\mutinfoatf#1#2#3{{\mutinfo_{#1}\paren{#2 ; #3}}} \def\renyientropy{\entropy} \def\renyientropyf#1#2{{\renyientropy_{#1}\paren{#2}}} \def\kolm{K} \def\kolmf#1{{\kolm\paren{#1}}} \def\ckolmf#1#2{{\kolm\paren{#1 \mid #2}}} \def\strlen#1{{\abs{#1}}} \def\fitproc{g} \def\fitprocf#1{{\fitproc\paren{#1}}} \def\fitmodf#1{{\fitted_{#1}}} \def\predvalf#1{{\fitted\paren{#1}}} \def\estmeanf#1{{\emuf{#1}}} \def\candproc#1{\fitproc_{#1}} \def\candproctuned#1{\fitproc^{#1}} \def\candproctunedf#1#2{{\candproctuned{#1}\paren{#2}}} \def\candfitted#1{{\fitted_{#1}}} \def\candpredvalf#1#2{{\candfitted{#1}\paren{#2}}} \def\fitmodvalf#1#2{{\fitmodf{#1}\paren{#2}}} \def\Epredvalf#1{{\Expfc{\trainset}{\predvalf{#1}}}} \def\Epredval{{\Expfc{\trainset}{\predval}}} \def\candfnset#1{\mathcal{G}_{#1}} \def\ncand{L} \def\icand{l} \def\nfolds{k} \def\ifold{j} \def\iobs{i} \def\obsidx{I} \def\nheld{m} \def\termfn#1{t_{#1}} \def\polydeg{d} \def\objfn{\mathcal{J}} \def\objfnf#1{{\objfn\paren{#1}}} \def\optalg{\mathcal{A}} \def\seed{\mathfrak{s}} \def\sscp{A} \def\newpredvar{\Predvar_{*}} \def\newoutvar{\Outvar_{*}} \def\newpredval{\predvar_{*}} \def\newoutval{\outvar_{*}} \def\predvari{\predvar_{\iobs}} \def\outvari{\outvar_{\iobs}} \def\heldpredvar#1{\Predvar_{*,#1}} \def\heldoutvar#1{\Outvar_{*,#1}} \def\heldpredval#1{\predvar_{*,#1}} \def\heldoutval#1{\outvar_{*,#1}} \def\posclass{{+}} \def\negclass{{-}} \def\ntp{n_{T\posclass}} \def\nfp{n_{F\posclass}} \def\nfn{n_{F\negclass}} \def\ntn{n_{T\negclass}} \def\given{\mid} \def\condE#1#2{{\E{#1 \given #2}}} \def\condVar#1#2{{\Var{#1 \given #2}}} \def\condCov#1#2#3{{\Cov{#1, #2 \given #3}}} \def\condPr#1#2{{\Prf{#1 \given #2}}} \def\condpmf#1#2{{\pmf{#1 \given #2}}} \def\condpdf#1#2{{\pdf\paren{#1 \given #2}}} \def\condcdf#1#2{{\cdff{#1 \given #2}}} \def\generr{\operatorname{Err}} \def\expgenerr#1#2{{\generr^{#1}\paren{#2}}} \def\cvest#1{\Est{\generr}_{\text{CV}(#1)}} \def\cvestof#1#2{\Est{\generr}^{#2}_{\text{CV}(#1)}} \def\cvestoff#1#2#3{{\cvestof{#1}{#2}\paren{#3}}} \def\fold#1{\mathcal{F}_{#1}} \def\foldsize#1{n_{#1}} \def\foldof#1{{\kappa\paren{#1}}} \def\fittedwo#1#2{{\fitted^{(-#1)}\paren{#2}}} \def\lev#1{h_{#1}} \def\foldmse#1{\MSEt_{#1}} \def\foldmseof#1#2{\MSEt^{#2}_{#1}} \def\foldmseoff#1#2#3{{\foldmseof{#1}{#2}\paren{#3}}} \def\cvse#1{\operatorname{SE}_{\text{CV}(#1)}} \def\cvseof#1#2{\operatorname{SE}^{#2}_{\text{CV}(#1)}} \def\cvseoff#1#2#3{{\cvseof{#1}{#2}\paren{#3}}} \def\rmselr#1{{\RMSEt\paren{#1}}} \def\epe#1#2#3{{\operatorname{EPE}^{#1}_{#2}\paren{#3}}} \def\epl#1#2#3{{\operatorname{EPL}^{#1}_{#2}\paren{#3}}} \def\termvec#1{\vecf{t}_{#1}} \def\trainerr{\overline{\operatorname{err}}} \def\valerr{\overline{\operatorname{err}}_{\text{val}}} \def\testerr{\overline{\operatorname{err}}_{\text{test}}} \def\arcoef{\rho} \def\truenulls{\mathcal{I}_0} \def\preimage#1#2{{{#1}^{-1}\paren{#2}}} \def\levelsetof#1#2{{\preimage{#2}{\cb{#1}}}} \def\predfn{f} \def\epredfn{\est{\predfn}} \def\predfnf#1{{\predfn\paren{#1}}} \def\epredfnf#1{{\epredfn\paren{#1}}} \def\cent#1{{#1}^{\mathrm{c}}} \def\aug#1{{#1}^{\mathrm{aug}}} \def\bestpredfn{\predfn^*} \def\bestpredfnf#1{{\bestpredfn\paren{#1}}} \def\predfam{\mathcal{Y}} \def\predfamof#1{\predfam_{#1}} \def\distfam{\mathcal{P}} \def\distfamof#1{\distfam_{#1}} \def\distmem{P} \def\distmemof#1{\distmem_{#1}} \def\edistmem{\est{\distmem}} \def\edistmemof#1{\edistmem_{#1}} \def\meanfnof#1{\mean_{#1}} \def\meanfnoff#1#2{{\meanfnof{#1}\paren{#2}}} \def\predval{\eoutvar} \def\vpredval{\veoutvar} \]

This page provides a searchable table of all macros defined in macros.qmd.