Characterizing Non-nesting for the Neyman-Pearson Family of Tests
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 provide...
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| Format: | Article |
| Language: | English |
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Springer
2016-11-01
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| Series: | Journal of Statistical Theory and Applications (JSTA) |
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| Online Access: | https://www.atlantis-press.com/article/25867322.pdf |
| _version_ | 1811292205091913728 |
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| author | Rahul Bhattacharya |
| author_facet | Rahul Bhattacharya |
| author_sort | Rahul Bhattacharya |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T04:41:56Z |
| format | Article |
| id | doaj.art-dbc5cfeab2eb451b802e866c6b260c14 |
| institution | Directory Open Access Journal |
| issn | 1538-7887 |
| language | English |
| last_indexed | 2024-04-13T04:41:56Z |
| publishDate | 2016-11-01 |
| publisher | Springer |
| record_format | Article |
| series | Journal of Statistical Theory and Applications (JSTA) |
| spelling | doaj.art-dbc5cfeab2eb451b802e866c6b260c142022-12-22T03:01:58ZengSpringerJournal of Statistical Theory and Applications (JSTA)1538-78872016-11-0115410.2991/jsta.2016.15.4.7Characterizing Non-nesting for the Neyman-Pearson Family of TestsRahul BhattacharyaFor 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.https://www.atlantis-press.com/article/25867322.pdfNested critical region; Most Powerful test |
| spellingShingle | Rahul Bhattacharya Characterizing Non-nesting for the Neyman-Pearson Family of Tests Journal of Statistical Theory and Applications (JSTA) Nested critical region; Most Powerful test |
| title | Characterizing Non-nesting for the Neyman-Pearson Family of Tests |
| title_full | Characterizing Non-nesting for the Neyman-Pearson Family of Tests |
| title_fullStr | Characterizing Non-nesting for the Neyman-Pearson Family of Tests |
| title_full_unstemmed | Characterizing Non-nesting for the Neyman-Pearson Family of Tests |
| title_short | Characterizing Non-nesting for the Neyman-Pearson Family of Tests |
| title_sort | characterizing non nesting for the neyman pearson family of tests |
| topic | Nested critical region; Most Powerful test |
| url | https://www.atlantis-press.com/article/25867322.pdf |
| work_keys_str_mv | AT rahulbhattacharya characterizingnonnestingfortheneymanpearsonfamilyoftests |