CSI 779, Spring 1995, J. E. Gentle

Assignment due April 17

This assignment is similar to a0410, except that we will study
confidence intervals for the variance in a normal distribution.  
The assignment is to conduct a study similar to that reported 
by Schenker in JASA 1988, pp 360 and 361.

We will use samples of size 20, 35, and 100 from a normal distribution
with varinace of 1.   We will use a nonparametric percentile, BCa and
ABC to set 90% confidence intervals, and estimate the coverage
probabilities using Monte Carlo.  Use bootstrap B = 1000 and Monte
Carlo M = 1000 (I just checked out the percentile method on my PC with
S-Plus, and it finished in a reasonable time.)

Prepare a two-way table:

          Coverages
 n    Percentile     BCa    ABC
 20      _%          _%     _%
 35      _%          _%     _%
100      _%          _%     _%

Explain the difference in the confidence intervals for the mean and
for the variance in terms of pivotal quantities 
(Efron & Tibshirani, p 161).

Email your solution to me.