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    On two-stage Monte Carlo tests of composite hypotheses

    Access Status
    Fulltext not available
    Authors
    Baddeley, Adrian
    Hardegen, A.
    Lawrence, T.
    Milne, R.
    Nair, G.
    Rakshit, Suman
    Date
    2017
    Type
    Journal Article
    
    Metadata
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    Citation
    Baddeley, A. and Hardegen, A. and Lawrence, T. and Milne, R. and Nair, G. and Rakshit, S. 2017. On two-stage Monte Carlo tests of composite hypotheses. Computational Statistics and Data Analysis. 114: pp. 75-87.
    Source Title
    Computational Statistics and Data Analysis
    DOI
    10.1016/j.csda.2017.04.003
    ISSN
    0167-9473
    School
    Department of Mathematics and Statistics
    Funding and Sponsorship
    http://purl.org/au-research/grants/arc/DP130102322
    http://purl.org/au-research/grants/arc/DP130104470
    URI
    http://hdl.handle.net/20.500.11937/63012
    Collection
    • Curtin Research Publications
    Abstract

    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.

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