Definition of a Statistic
In many problems in which a parameter 0 must be estimated. it is possible to find either an M.L.E. or a Bayes estimator that will be suitable. In some problems, however, neither of these estimators may be suitable. There may not be any MLE. or there many be more than one. Even when an M.LE. is unique. it may not be a suitable estimator, as in Example 6.5.5, where the MLE. always underestimates the value of 0. Reasons why there may not be suitable Bayes estimator were presented at the end of Section 6.4 in such problems, the search for a good estimator must be extended beyond the methods that have been introduced thus far.