Consider a simulated dataset with a binary response $`$y$`$ and $$5000$$ predictors measured on $n $=50$$ cases, saved as a matrix $`$x$`.$

$```\{$r$\}$

set.seed$(1)$

y $<-$ c$($rep$("$c$1",25),$ rep$("$c$2",25))$

x $<-$ matrix$($NA$,$ nrow $=50,$ ncol $=5000)$

for $($i in $1$:$5000)\{$

x$[,$ i$]<-$ rnorm$(50)$

$\}$

$```$

A simple classifier is applied to the simulated dataset, where the classification is performed in two steps:

$*$ Step $1.$ Feature selection: Select $$20$$ predictors with smallest $p$$-$values from two$-$sample $t$$-$tests

$*$ Step $2.$ Model fitting: Fit a linear discriminant analysis $($LDA$)$ model, using only these $$20$$ selected predictors.

We would like to compute the $$5$$$-$fold cross$-$validation $($CV$)$ estimate of test accuracy rate for the classifier.