Due Date
Due Fri, Nov 01, 2013.
Problems From Efron and Tibshirani
Problems 4.1, 4.2, 5.2, and 5.4.
Additional Problem
The file
contains two variables x
, which is a random sample from a
normal distribution, and y
, which is a random sample from
a Cauchy distribution.
 For the variable
x
compute the sample mean
 the sample median
 the sample 25% trimmed mean, for which R statement is
mean(x, trim=0.25)
And for each of these three point estimates calculate a bootstrap standard error (use bootstrap sample size 1000 at least).
 Repeat part (a) for the variable
y

Using the fact that
x
is actually a random sample from a normal distribution, we actually know the asymptotic relative efficiency (ARE) of estimators (i) and (ii) in part (a). (See the efficiency page for details). What is it, and how close is the square of the ratio of bootstrap standard errors? 
Using the fact that
y
is actually a random sample from a Cauchy distribution, also denoted t(1) because it is the Student t distribution for one degree of freedom, we actually know the asymptotic relative efficiency (ARE) of estimators (i) and (ii) in part (b). (See the efficiency page for details). What is it, and how close is the square of the ratio of bootstrap standard errors?
Answers
Answers in the back of the book
for the additional problem are here.