\frametitle {Numerical comparison}
\begin{block}{}
{\footnotesize
\begin{verbatim}
sd <- 1
n <- 200 ; x <- rnorm(n=n,mean=2,sd=sd)
B <- 10000
X.theo <- X.boot <- matrix(nrow=n,ncol=B)
for(b in 1:B)
  {
    X.theo[,b] <- rnorm(n=n,mean=2,sd=1)
    X.boot[,b] <- sample(x=x,size=n,replace=TRUE)
  }
mean.theo <- apply(X=X.theo,MARGIN=2,FUN=mean)
mean.boot <- apply(X=X.boot,MARGIN=2,FUN=mean)
par(mfrow=c(1,2))
hist(mean.theo,prob=TRUE)
lines(density(mean.theo),col=2,lwd=2); lines(density(mean.boot),lwd=2,col=3)
hist(mean.boot,prob=TRUE)
lines(density(mean.theo),col=2,lwd=2); lines(density(mean.boot),lwd=2,col=3)
var(mean.theo)
var(mean.boot)
sd^2/n # truth
\end{verbatim}
}
\end{block}