Compare the non parametric confidence interval for the variance obtained from using the functional delta method to the normal-theory interval: (n 1)s 2 2 1/2,n1 , (n 1)s 2 2 /2,n1 ! where s 2 is the (unbiased) sample variance. Conduct a simulation study to determine the coverage probability and average interval width of these two intervals.

a

Carry out the above simulation with data generated from the standard normal distribution.

b

Repeat using data generated from an exponential distribution with rate 1.

c

Briefly, comment on the strengths and weaknesses of these two methods.

"NEED R PROGRAMMING CODE FOR SIMULATIONS"