Power in high-dimensional testing problems
Fan et al. (2015) recently introduced a remarkable method for increasing asymptotic power of tests in high-dimensional testing problems. If applicable to a given test, their power enhancement principle leads to an improved test that has the same asymptotic size, uniformly non-inferior asymptotic pow...
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| Format: | Journal article |
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Econometric Society
2019
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| _version_ | 1797087235166699520 |
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| author | Kock, A Preinerstorfer, D |
| author_facet | Kock, A Preinerstorfer, D |
| author_sort | Kock, A |
| collection | OXFORD |
| description | Fan et al. (2015) recently introduced a remarkable method for increasing asymptotic power of tests in high-dimensional testing problems. If applicable to a given test, their power enhancement principle leads to an improved test that has the same asymptotic size, uniformly non-inferior asymptotic power, and is consistent against a strictly broader range of alternatives than the initially given test. We study under which conditions this method can be applied and show the following: In asymptotic regimes where the dimensionality of the parameter space is fixed as sample size increases, there often exist tests that can not be further improved with the power enhancement principle. However, when the dimensionality of the parameter space increases sufficiently slowly with sample size and a marginal local asymptotic normality (LAN) condition is satisfied, every test with asymptotic size smaller than one can be improved with the power enhancement principle. While the marginal LAN condition alone does not allow one to extend the latter statement to all rates at which the dimensionality increases with sample size, we give sufficient conditions under which this is the case. |
| first_indexed | 2024-03-07T02:32:55Z |
| format | Journal article |
| id | oxford-uuid:a7d98c89-69cd-4c0d-8e58-efc8d1af34f7 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T02:32:55Z |
| publishDate | 2019 |
| publisher | Econometric Society |
| record_format | dspace |
| spelling | oxford-uuid:a7d98c89-69cd-4c0d-8e58-efc8d1af34f72022-03-27T02:57:15ZPower in high-dimensional testing problemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a7d98c89-69cd-4c0d-8e58-efc8d1af34f7Symplectic Elements at OxfordEconometric Society2019Kock, APreinerstorfer, DFan et al. (2015) recently introduced a remarkable method for increasing asymptotic power of tests in high-dimensional testing problems. If applicable to a given test, their power enhancement principle leads to an improved test that has the same asymptotic size, uniformly non-inferior asymptotic power, and is consistent against a strictly broader range of alternatives than the initially given test. We study under which conditions this method can be applied and show the following: In asymptotic regimes where the dimensionality of the parameter space is fixed as sample size increases, there often exist tests that can not be further improved with the power enhancement principle. However, when the dimensionality of the parameter space increases sufficiently slowly with sample size and a marginal local asymptotic normality (LAN) condition is satisfied, every test with asymptotic size smaller than one can be improved with the power enhancement principle. While the marginal LAN condition alone does not allow one to extend the latter statement to all rates at which the dimensionality increases with sample size, we give sufficient conditions under which this is the case. |
| spellingShingle | Kock, A Preinerstorfer, D Power in high-dimensional testing problems |
| title | Power in high-dimensional testing problems |
| title_full | Power in high-dimensional testing problems |
| title_fullStr | Power in high-dimensional testing problems |
| title_full_unstemmed | Power in high-dimensional testing problems |
| title_short | Power in high-dimensional testing problems |
| title_sort | power in high dimensional testing problems |
| work_keys_str_mv | AT kocka powerinhighdimensionaltestingproblems AT preinerstorferd powerinhighdimensionaltestingproblems |