Macro Reference

\[ \def\cbl#1{\mathopen{}\left\{#1\right.} \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\sb#1{\mathopen{}\left[#1\right]\mathclose{}} \def\distop{\operatorname} \def\sbmat#1{\begin{bmatrix}#1\end{bmatrix}} \def\Prf#1{\Pr\paren{#1}} \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{\distop{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{\mathopen{}\left\lceil#1\right\rceil\mathclose{}} \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\vb{\vec \b} \def\v0{\vec{0}} \def\vzero{\vec{0}} \def\gb{\beta} \def\gg{\gamma} \def\gd{\delta} \def\eps{\varepsilon} \def\veps{\vec{\varepsilon}} \def\epsp#1{\eps\paren{#1}} \def\epsf#1{\eps\paren{#1}} \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\hb{\hat \beta} \def\hvb{\hat{\vb}} \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\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\th{\theta} \def\vth{\vec{\theta}} \def\Th{\Theta} \def\xbar{\bar{x}} \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\loglik{\ell} \def\logl{\ell} \def\llikf#1{\llik \paren{#1}} \def\Likf#1{\Lik\paren{#1}} \def\loglikf{\llikf} \def\loglf{\llikf} \def\likf{\llikf} \def\deviation{e} \def\devn{\deviation} \def\deviationv{\vec{\deviation}} \def\devnv{\deviationv} \def\Deviation{E} \def\Devn{\Deviation} \def\residual{r} \def\resid{\residual} \def\Residual{R} \def\Resid{\Residual} \def\stdresidual{r^\prime} \def\stdresid{\stdresidual} \def\StdResidual{R^\prime} \def\StdResid{\StdResidual} \def\modresidual{r^*} \def\modresid{\modresidual} \def\ModResidual{R^*} \def\ModResid{\ModResidual} \def\score{\ell'} \def\scorev{\vec{\ell'}} \def\scorei{\vec{\ell_i'}} \def\scorevi{\vec{\ell_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#1{\hess \paren{#1}} \def\starf#1{#1^*} \def\lik{\ell} \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\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#1#2{\derivf{#1}{#2}} \def\derivfdn#1#2{\derivff{#1}{#2}} \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\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{\operatorname{E}}}\nolimits\sb{#1}} \def\hExp#1{\mathop{\hat{\operatorname{E}}}\nolimits\sb{#1}} \def\hExpf#1{\mathop{\hat{\operatorname{E}}}\nolimits\sb{#1}} \def\hmu{\hat{\mu}} \def\hmuf#1{\hmu\paren{#1}} \def\Expp{\distop{E}} \def\Ep{\distop{E}} \def\expit{\operatorname{expit}} \def\expitf#1{\expit\cb{#1}} \def\dexpitf#1{\expit'\cb{#1}} \def\logit{\operatorname{logit}} \def\logitf#1{\logit\cb{#1}} \def\E#1{\distop{E}\sb{#1}} \def\Ef#1{\distop{E}\sb{#1}} \def\Exp#1{\distop{E}\sb{#1}} \def\Expf#1{\distop{E}\sb{#1}} \def\Expfc#1#2{\distop{E}_{#1}\sb{#2}} \def\evalAt#1#2{\left.{#1}\right|_{#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#1{\operatorname{Var}\paren{#1}} \def\Var#1{\operatorname{Var}\paren{#1}} \def\hVar#1{\mathop{\widehat{\operatorname{Var}}}\nolimits\paren{#1}} \def\Varf#1{\operatorname{Var}\paren{#1}} \def\hvarf#1{\hvart\paren{#1}} \def\Cov#1{\Covt \paren{#1}} \def\Covs#1#2{\Covt \paren{#1, #2}} \def\Covf#1{\Covt \paren{#1}} \def\covh#1{\hcovt\paren{#1}} \def\covhf#1{\hcovt\paren{#1}} \def\hcovf#1{\hcovt\paren{#1}} \def\Cort{\operatorname{Cor}} \def\hcort{\mathop{\widehat{\Cort}}\nolimits} \def\Cor#1{\Cort \paren{#1}} \def\Corf#1{\Cort \paren{#1}} \def\Cors#1#2{\Cort \paren{#1, #2}} \def\hCor#1{\hcort\paren{#1}} \def\hCorf#1{\hcort\paren{#1}} \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#1{\varht\paren{#1}} \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#1{\mathop{\widehat{\operatorname{SD}}}\nolimits\paren{#1}} \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#1{\operatorname{se}\paren{#1}} \def\hse#1{\hset\paren{#1}} \def\hsef#1{\hset\paren{#1}} \def\SE#1{\operatorname{SE}\paren{#1}} \def\SEf#1{\operatorname{SE}\paren{#1}} \def\SDf#1{\operatorname{SD}\paren{#1}} \def\HSE#1{\hSE\paren{#1}} \def\hSEf#1{\hSE\paren{#1}} \def\logt{\operatorname{log}} \def\logf#1{\logt\cb{#1}} \def\dlog{\logt'} \def\dlogf#1{\dlog \cb{#1}} \renewcommand{\exp}[1]{\operatorname{exp}\cb{#1}} \def\expt{\operatorname{exp}} \def\expf#1{\operatorname{exp}\cb{#1}} \def\expfn#1{\expf{#1}} \def\dexp{\operatorname{exp}'} \def\dexpf#1{\dexp \cb{#1}} \def\e#1{\text{e}^{#1}} \def\ef#1{\text{e}^{#1}} \def\inv#1{\mathopen{}\left(#1\right)^{-1}\mathclose{}} \def\invf#1{\mathopen{}\left(#1\right)^{-1}\mathclose{}} \def\invp#1{\mathopen{}\left(#1\right)^{-1}\mathclose{}} \def\invcb#1{\mathopen{}\left\{#1\right\}^{-1}\mathclose{}} \def\invsb#1{\mathopen{}\left[#1\right]^{-1}\mathclose{}} \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#1{\mathbb{1}_{#1}} \def\set#1{\cb{#1}} \def\pf#1{\p \paren{#1}} \def\Pf#1{\P \paren{#1}} \def\Bias#1{\operatorname{Bias}\paren{#1}} \def\bias#1{\operatorname{Bias}\paren{#1}} \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{\mathopen{}\left\lVert#1\right\rVert^2\mathclose{}} \def\sqf#1{\mathopen{}\left(#1\right)^2\mathclose{}} \def\sq{^2} \def\err{\eps} \def\erf#1{\err\paren{#1}} \renewcommand{\vec}[1]{\tilde{#1}} \def\vecf#1{\tilde{#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{{\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\vz{\vecf{z}} \def\vZ{\vecf{Z}} \def\vD{\vecf{D}} \def\vd{\vecf{d}} \def\vT{\vecf{T}} \def\vt{\vecf{t}} \def\v1{\vec{1}} \def\vpi{\vecf{\pi}} \def\mat#1{\mathbf{#1}} \def\dsn#1{#1_1, \ldots, #1_n} \def\X1n{\dsn{X}} \def\Xin{\dsn{X}} \def\x1n{\dsn{x}} \def\y1n{\dsn{y}} \def\'{^{\top}} \def\pt#1{\paren{#1}\'} \def\tp#1{{#1}\'} \def\dpr{\cdot} \def\Xx1n{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\iprod#1#2{\left\langle #1, #2 \right\rangle} \def\iprodf{\iprod} \def\oprod#1#2{#1 \tp{#2}} \def\stprod#1{\tprod{#1}{#1}} \def\siprod#1{\iprod{#1}{#1}} \def\soprod#1{#1 \tp{#1}} \def\sdprod#1{\dprod{#1}{#1}} \def\sdprodf{\sdprod} \def\dsvn#1#2{#1_1=#2_1, \ldots, #1_n = #2_n} \def\sumn#1{\sum_{#1=1}^n} \def\sumin{\sum_{i=1}^n} \def\sumiN{\sum_{i=1}^N} \def\sumip{\sum_{i=1}^p} \def\sumjn{\sum_{j=1}^n} \def\sumjp{\sum_{j=1}^p} \def\sumi1n{\sum_{i=1}^n} \def\prodin{\prod_{i=1}^n} \def\prodi1n{\prod_{i=1}^n} \def\lp#1{\dprodf{#1}{\vb}} \def\lpdp{\lp{\vx}} \def\lincomp{\eta} \def\odds{\omega} \def\OR{\operatorname{OR}} \def\ratio{\theta} \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{\distop{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\'} \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{r} \def\stdresid{r'} \def\modresid{r^*} \def\ub{\underbrace} \def\ubf#1#2{\ub{#1}_{#2}} \def\dims#1#2{\ub{#1}_{#2}} \def\residv{\vec{r}} \def\hprob{\hat{\prob}} \def\hprobs{\hprob} \def\hrisk{\hprob} \def\hprev{\hprob} \def\hodds{\hat{\odds}} \def\hrate{\hat{\rate}} \def\hhaz{\hrate} \def\hcuhaz{\hat{\cuhaz}} \def\hcumhaz{\hcuhaz} \def\hratio{\hat{\ratio}} \def\hratiof#1{\hratio\paren{#1}} \def\hror{\hat{\ror}} \def\horf#1{\hror\paren{#1}} \def\hhazratio{\hat{\hazratio}} \def\hhr{\hhazratio} \def\hrhaz{\hhazratio} \def\hhazr{\hhazratio} \def\hhrf#1{\hhazratio\paren{#1}} \def\hrhazf{\hhrf} \def\hhazrf{\hhrf} \def\hrateratio{\hat{\rateratio}} \def\hrater{\hrateratio} \def\hrrate{\hrateratio} \def\hrateratiof#1{\hrateratio\paren{#1}} \def\hraterf{\hrateratiof} \def\hrratef{\hrateratiof} \def\hriskratio{\hat{\riskratio}} \def\hrrisk{\hriskratio} \def\hriskr{\hriskratio} \def\hriskratiof#1{\hriskratio\paren{#1}} \def\hrriskf{\hriskratiof} \def\hriskrf{\hriskratiof} \def\hprevratio{\hat{\prevratio}} \def\hprr{\hprevratio} \def\hprevratiof#1{\hprevratio\paren{#1}} \def\hprrf{\hprevratiof} \def\hsurvratio{\hat{\survratio}} \def\hrsurv{\hsurvratio} \def\hsurvr{\hsurvratio} \def\hsurvratiof#1{\hsurvratio\paren{#1}} \def\hrsurvf{\hsurvratiof} \def\hsurvrf{\hsurvratiof} \def\hcuhazratio{\hat{\cuhazratio}} \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{\hat{\oddsfactor}} \def\hoddsfactorf#1{\hoddsfactor\paren{#1}} \def\hfodds{\hoddsfactor} \def\hfoddsf{\hoddsfactorf} \def\hoddsff{\hoddsfactorf} \def\hhazfactor{\hat{\hazfactor}} \def\hhazfactorf#1{\hhazfactor\paren{#1}} \def\hfhaz{\hhazfactor} \def\hfhazf{\hhazfactorf} \def\hhazff{\hhazfactorf} \def\hratefactor{\hat{\ratefactor}} \def\hratefactorf#1{\hratefactor\paren{#1}} \def\hfrate{\hratefactor} \def\hfratef{\hratefactorf} \def\hrateff{\hratefactorf} \def\hriskfactor{\hat{\riskfactor}} \def\hriskfactorf#1{\hriskfactor\paren{#1}} \def\hfrisk{\hriskfactor} \def\hfriskf{\hriskfactorf} \def\hriskff{\hriskfactorf} \def\hprevfactor{\hat{\prevfactor}} \def\hprevfactorf#1{\hprevfactor\paren{#1}} \def\hfprev{\hprevfactor} \def\hfprevf{\hprevfactorf} \def\hprevff{\hprevfactorf} \def\hcuhazfactor{\hat{\cuhazfactor}} \def\hcuhazfactorf#1{\hcuhazfactor\paren{#1}} \def\hfcuhaz{\hcuhazfactor} \def\hfcuhazf{\hcuhazfactorf} \def\hcuhazff{\hcuhazfactorf} \def\hsurvfactor{\hat{\survfactor}} \def\hsurvfactorf#1{\hsurvfactor\paren{#1}} \def\hfsurv{\hsurvfactor} \def\hfsurvf{\hsurvfactorf} \def\hsurvff{\hsurvfactorf} \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\evb{\est{\vb}} \def\eR{\est{R}} \def\ek{\est{\kappa}} \def\ekappa{\est{\kappa}} \def\el{\est{\lambda}} \def\ey{\est{y}} \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{\operatorname{E}}}\nolimits\sb{#1}} \def\eExp#1{\mathop{\est{\operatorname{E}}}\nolimits\sb{#1}} \def\eExpf#1{\mathop{\est{\operatorname{E}}}\nolimits\sb{#1}} \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#1{\ecort\paren{#1}} \def\eCors#1#2{\ecort\paren{#1, #2}} \def\eSD#1{\mathop{\Est{\operatorname{SD}}}\nolimits\paren{#1}} \def\eSDf#1{\mathop{\Est{\operatorname{SD}}}\nolimits\paren{#1}} \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#1{\eset\paren{#1}} \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\eprob{\est{\prob}} \def\eprobs{\eprob} \def\erisk{\eprob} \def\eprev{\eprob} \def\eodds{\est{\odds}} \def\erate{\est{\rate}} \def\ehaz{\erate} \def\ecuhaz{\est{\cuhaz}} \def\ecumhaz{\ecuhaz} \def\eratio{\est{\ratio}} \def\eratiof#1{\eratio\paren{#1}} \def\eror{\est{\ror}} \def\eorf#1{\eror\paren{#1}} \def\ehazratio{\est{\hazratio}} \def\ehr{\ehazratio} \def\erhaz{\ehazratio} \def\ehazr{\ehazratio} \def\ehrf#1{\ehazratio\paren{#1}} \def\erhazf{\ehrf} \def\ehazrf{\ehrf} \def\erateratio{\est{\rateratio}} \def\erater{\erateratio} \def\errate{\erateratio} \def\erateratiof#1{\erateratio\paren{#1}} \def\eraterf{\erateratiof} \def\erratef{\erateratiof} \def\eriskratio{\est{\riskratio}} \def\errisk{\eriskratio} \def\eriskr{\eriskratio} \def\eriskratiof#1{\eriskratio\paren{#1}} \def\erriskf{\eriskratiof} \def\eriskrf{\eriskratiof} \def\eprevratio{\est{\prevratio}} \def\eprr{\eprevratio} \def\eprevratiof#1{\eprevratio\paren{#1}} \def\eprrf{\eprevratiof} \def\esurvratio{\est{\survratio}} \def\ersurv{\esurvratio} \def\esurvr{\esurvratio} \def\esurvratiof#1{\esurvratio\paren{#1}} \def\ersurvf{\esurvratiof} \def\esurvrf{\esurvratiof} \def\ecuhazratio{\est{\cuhazratio}} \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{\est{\oddsfactor}} \def\eoddsfactorf#1{\eoddsfactor\paren{#1}} \def\efodds{\eoddsfactor} \def\efoddsf{\eoddsfactorf} \def\eoddsff{\eoddsfactorf} \def\ehazfactor{\est{\hazfactor}} \def\ehazfactorf#1{\ehazfactor\paren{#1}} \def\efhaz{\ehazfactor} \def\efhazf{\ehazfactorf} \def\ehazff{\ehazfactorf} \def\eratefactor{\est{\ratefactor}} \def\eratefactorf#1{\eratefactor\paren{#1}} \def\efrate{\eratefactor} \def\efratef{\eratefactorf} \def\erateff{\eratefactorf} \def\eriskfactor{\est{\riskfactor}} \def\eriskfactorf#1{\eriskfactor\paren{#1}} \def\efrisk{\eriskfactor} \def\efriskf{\eriskfactorf} \def\eriskff{\eriskfactorf} \def\eprevfactor{\est{\prevfactor}} \def\eprevfactorf#1{\eprevfactor\paren{#1}} \def\efprev{\eprevfactor} \def\efprevf{\eprevfactorf} \def\eprevff{\eprevfactorf} \def\ecuhazfactor{\est{\cuhazfactor}} \def\ecuhazfactorf#1{\ecuhazfactor\paren{#1}} \def\efcuhaz{\ecuhazfactor} \def\efcuhazf{\ecuhazfactorf} \def\ecuhazff{\ecuhazfactorf} \def\esurvfactor{\est{\survfactor}} \def\esurvfactorf#1{\esurvfactor\paren{#1}} \def\efsurv{\esurvfactor} \def\efsurvf{\esurvfactorf} \def\esurvff{\esurvfactorf} \]

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