Bootsrap
x = rnorm(50)
mx=mean(x); vx=var(x);mex=median(x); q25=quantile(x,prob=0.25)
c(mx,mex,vx,q25)
## 25%
## 0.0599227 0.1059769 0.7431852 -0.6485951
m=length(x); B=500; bmx=bvx=bq25=bmex=rep(0,B)
for(i in 1:B){
si=sample(x,size=m,replace=T)
bmx[i]=mean(si)
bmex[i]=median(si)
bq25[i]=quantile(si,prob=0.25)
bvx[i]=var(si)
}
par(mfrow=c(2,2))
hist(bmx,xlab="",main="Mean"); abline(v=mx,col=2)
hist(bvx,xlab="",main="Variance"); abline(v=vx,col=2)
hist(bmex,xlab="",main="Median"); abline(v=mex,col=2)
hist(bq25,xlab="",main="25% quantile"); abline(v=q25,col=2)
Bootstrap estimation of bias
Bootstrap estimation of variance
Bootsrap confidence intervals