ABSTRACT
Statistical inference can generally be viewed as making a conclusion about an underlying random process from the data generated by it. Any conclusion is essentially a decision and, therefore, statistical inference can be considered as a decision making process under uncertainty based on analysis of data. The three main problems of statistical inference, namely, point estimation, confidence intervals, and hypothesis testing, fall within a general statistical decision theory framework. It seems obvious that only admissible rules should be of interest, though there exist particular examples where admissible rules are somewhat ad-hoc, while one can find an intuitively clear and simple inadmissible procedure. Usually, however, it is quite rare that one “reasonable” rule is uniformly better than another “reasonable” one. The minimax criterion is very conservative, where one wants to ensure a maximal protection only in the worst case essentially ignoring all other possible scenarios.
