On two-stage Monte Carlo tests of composite hypotheses
A major weakness of the classical Monte Carlo test is that it is biased when the null hypothesis is composite. This problem persists even when the number of simulations tends to infinity. A standard remedy is to perform a double bootstrap test involving two stages of Monte Carlo simulation: under su...
| Main Authors: | , , , , , |
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| Format: | Journal Article |
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Elsevier Science
2017
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| Online Access: | http://purl.org/au-research/grants/arc/DP130102322 http://hdl.handle.net/20.500.11937/63012 |
| _version_ | 1848760970614145024 |
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| author | Baddeley, Adrian Hardegen, A. Lawrence, T. Milne, R. Nair, G. Rakshit, Suman |
| author_facet | Baddeley, Adrian Hardegen, A. Lawrence, T. Milne, R. Nair, G. Rakshit, Suman |
| author_sort | Baddeley, Adrian |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | A major weakness of the classical Monte Carlo test is that it is biased when the null hypothesis is composite. This problem persists even when the number of simulations tends to infinity. A standard remedy is to perform a double bootstrap test involving two stages of Monte Carlo simulation: under suitable conditions, this test is asymptotically exact for any fixed significance level. However, the two-stage test is shown to perform poorly in some common applications: for a given number of simulations, the test with the smallest achievable significance level can be strongly biased. A 'balanced' version of the two-stage test is proposed, which is exact, for all achievable significance levels, when the null hypothesis is simple, and which performs well for composite null hypotheses. |
| first_indexed | 2025-11-14T10:24:14Z |
| format | Journal Article |
| id | curtin-20.500.11937-63012 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:24:14Z |
| publishDate | 2017 |
| publisher | Elsevier Science |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-630122022-10-06T07:02:29Z On two-stage Monte Carlo tests of composite hypotheses Baddeley, Adrian Hardegen, A. Lawrence, T. Milne, R. Nair, G. Rakshit, Suman A major weakness of the classical Monte Carlo test is that it is biased when the null hypothesis is composite. This problem persists even when the number of simulations tends to infinity. A standard remedy is to perform a double bootstrap test involving two stages of Monte Carlo simulation: under suitable conditions, this test is asymptotically exact for any fixed significance level. However, the two-stage test is shown to perform poorly in some common applications: for a given number of simulations, the test with the smallest achievable significance level can be strongly biased. A 'balanced' version of the two-stage test is proposed, which is exact, for all achievable significance levels, when the null hypothesis is simple, and which performs well for composite null hypotheses. 2017 Journal Article http://hdl.handle.net/20.500.11937/63012 10.1016/j.csda.2017.04.003 http://purl.org/au-research/grants/arc/DP130102322 http://purl.org/au-research/grants/arc/DP130104470 Elsevier Science restricted |
| spellingShingle | Baddeley, Adrian Hardegen, A. Lawrence, T. Milne, R. Nair, G. Rakshit, Suman On two-stage Monte Carlo tests of composite hypotheses |
| title | On two-stage Monte Carlo tests of composite hypotheses |
| title_full | On two-stage Monte Carlo tests of composite hypotheses |
| title_fullStr | On two-stage Monte Carlo tests of composite hypotheses |
| title_full_unstemmed | On two-stage Monte Carlo tests of composite hypotheses |
| title_short | On two-stage Monte Carlo tests of composite hypotheses |
| title_sort | on two-stage monte carlo tests of composite hypotheses |
| url | http://purl.org/au-research/grants/arc/DP130102322 http://purl.org/au-research/grants/arc/DP130102322 http://hdl.handle.net/20.500.11937/63012 |