Question

Obtain the jackknife estimates of bias and standard error of ˆθ^.

3, 5, 7, 18, 43, 85, 91, 98, 100, 130, 230, 487.

Use R software

Answer 1

Sol:

Rcode:

library(bootstrap)
est <- c(3, 5, 7, 18, 43, 85, 91, 98, 100, 130, 230, 487)
res<- jackknife(est, median)
c(res$jack.bias, res$jack.se)

Output:

0.000000 9.949874

Also alternatively use can also use

library(UsingR)
x <- est
n <- length(x)
theta <- median(x)
jk <- sapply(1 : n,
function(i) median(x[-i])
)
thetaBar <- mean(jk)
biasEst <- (n - 1) * (thetaBar - theta)
seEst <- sqrt((n - 1)* mean((jk - thetaBar)^2))

c(biasEst, seEst)

jack knife estimate of bias is 0

jack knife estimate of standard error is 9.949874