Bootstrap vs. Jackknife Variance Estimates

# Simulate n standard normal random variables
n=20
set.seed(11)
x <- rnorm(n,0,1) 
options(warn=-1)



#Bootstrap
#load(boot)
boot <-numeric(200)   #specifies a vector of real values length 200
  for (i in 1:2000){
    boot[i]<- sample(x, replace=T)
  }
hist(boot, col= "light blue", main="Histogram of Bootstrap ReSampling")

mean(boot)

## [1] -0.3611196

var(boot)

## [1] 0.6585006

#Jackknife

jack <- numeric(length(x)-1)
pseudo <- numeric(length(x))
for (j in 1:length(x)) {
    if(j < i) jack[j] <- x[j]
    else if(j > i) Jack[j-1] <- x[j] }
pseudo[i] <- length(x)*sample(x, replace=T) -(length(x)-1)*sample(jack, replace=T)
Jack <- numeric(length(x)-1)
pseudo <- numeric(length(x))
for (i in 1:length(x))
  {for (j in 1:length(x))
  {if(j < i) jack[j] <- x[j] else if(j > i) jack[j-1] <- x[j]
    } 
  pseudo[i] <- length(x)*sample(x, replace=T) -(length(x)-1)*sample(jack, replace=T)
}
hist(jack, col = "light green", main="Histogram of Jackknife ReSampling")

mean(jack)

## [1] -0.3495979

var(jack)

## [1] 0.718789

# Compare variance estimates between Bootstrap & Jackknife
simulation.variance <- c(var(boot), var(jack))
simulation.variance

## [1] 0.6585006 0.7187890