Characterizing Non-nesting for the Neyman-Pearson Family of Tests

DOI

10.2991/jsta.2016.15.4.7How to use a DOI?

Keywords

Nested critical region; Most Powerful test

Abstract

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.

Copyright

© 2017, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Rahul Bhattacharya
PY  - 2016
DA  - 2016/12/01
TI  - Characterizing Non-nesting for the Neyman-Pearson Family of Tests
JO  - Journal of Statistical Theory and Applications
SP  - 400
EP  - 404
VL  - 15
IS  - 4
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.2016.15.4.7
DO  - 10.2991/jsta.2016.15.4.7
ID  - Bhattacharya2016
ER  -