Resampling student'st-type statistics |
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Authors: | Arnold Janssen |
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Institution: | 1. Mathematisches Institut, Universit?t Düsseldorf, Universit?tsstr. 1, D-40225, Düsseldorf, Germany
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Abstract: | The present paper establishes conditional and unconditional central limit theorems for various resampling procedures for thet-statistic. The results work under fairly general conditions and the underlying random variables need not to be independent.
Specific examples are then them(n) (double) bootstrap out ofk(n) observations, the Bayesian bootstrap and two-samplet-type permutation statistics. In case whenm(n)/k(n) is bounded away from zero and infinity necessary and sufficient conditions for the conditional central limit law of the bootstrapt-statistics are established. For high resampling intensity whenm(n)/k(n) tends to infinity the following general result is obtained. Without further other assumptions the bootstrap makes the resampledt-statistic automatically normal. The results are based on a general conditional limit theorem for weighted resampling statistics
which is of own interest. |
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Keywords: | Student'st-statistic Welch statistic two-sample permutation statistic weighted bootstrap double bootstrap Bayesian bootstrap central limit theorem conditional central limit theorem |
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