COMPARISON OF LOCATION ESTIMATORS USING BANKS' CRITERION

In this paper, we analyze further Banks' (1997) closeness criterion for estimators, which is an alternative to Pitman's (1937) closeness criterion. We mainly concentrate our analysis on location estimation, and justify a conjecture by Banks (1997) that for heavy tail distributions the sample median is better than the sample mean when estimating a location parameter. The conlusion is reversed for distributions with lighter tails. To achieve this, we use asymptotics and exact probability calculations.