The Empirical Distribution Function and the Best Invariant Estimator: Which is Admissible and Which is Minimax?

摘要

In this thesis, we review the empirical distribution function and best invariant estimators. We go on to identify some of the basic properties of each. Then, we consider the section of decision theory involving loss functions to explain admissibility and minimaxity. These two particularly interesting properties will be explained thoroughly and some basic examples will be given. This will be done to form a base in order to review several papers written about admissibility and minimaxity of both the empirical distribution function and best invariant estimators.