Jackknife

#jackknife - 1
theta.hat <- cor(dat$newpatch, dat$oldpatch)
n <- nrow(dat);n

theta.hat.minus <- numeric(n)
for(i in 1:n){
  theta.hat.minus[i] <- cor(dat$newpatch[-i], dat$oldpatch[-i])
}
theta.hat.minus

bias.jack <- (n-1)*(mean(theta.hat.minus) - theta.hat);bias.jack
theta.jack <- theta.hat - bias.jack;theta.jack

theta.hat.star.minus <- n*theta.hat - (n-1)*theta.hat.minus
mean(theta.hat.star.minus)

se <- sqrt((n-1)*mean((theta.hat.minus - mean(theta.hat.minus))^2));se

 

#jackknofe - 2

library(bootstrap)
dat <- law;dat

 

theta.hat <- cor(dat$LSAT, dat$GPA)
n <- nrow(dat);n
theta.hat.minus <- numeric(n)
for(i in 1:n){
  theta.hat.minus[i] <- cor(dat$LSAT[-i], dat$GPA[-i])
}

bias.jack <- (n-1)*(mean(theta.hat.minus) - theta.hat)
se.jack <- sqrt((n-1)*mean((theta.hat.minus - mean(theta.hat.minus))^2))