期刊名称：Journal of Statistical Theory and Applications (JSTA)
电子版ISSN：1538-7887
出版年度：2016
卷号：15
期号：4
页码：402-406
DOI：10.2991/jsta.2016.15.4.7
语种：English
出版社：Atlantis Press
摘要：For testing a simple null hypothesis against a simple alternative using Neyman-Pearson theory, examples of most powerful non-randomized critical regions are constructed, which are overlapping for varying sizes. A likelihood ratio based criterion, characterizing such critical regions, is also provided. A simple method, in addition, is suggested to construct the class of distributions providing overlapping critical regions for unequal sizes. These examples, in fact, counterexamples are important in explaining the fact that power of an optimum test may not increase with an increase in size.
