Expand the comparisons made in Example 10.3.7.
(a) Another test based on Huber's M-estimator would be one that used a variance estimate, based on (10.3.6). Examine the performance of such a test statistic, and comment on its desirability (or lack of) as an alternative to either (10.3.8) or (10.3.9).
(b) Another test based on Huber's M-estimator would be one that used a variance from a bootstrap calculation. Examine the performance of such a test statistic.
(c) A robust competitor to θM is the median. Examine the performance of tests of a location parameter based on the median.