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A Monte-Carlo comparison of Studentized bootstrap and permutation tests for heteroscedastic two-sample problems. (English) Zbl 1091.62034

Different tests for a two-sample problem of the Behrens-Fisher type are considered including the classical Welch, the Studentized permutation, the Studentized bootstrap, and the prepivoted bootstrap tests. They are compared via simulations for samples from normal, double exponential, exponential, uniform, and Cauchy distributions. True significance levels and power of the tests are evaluated for the nominal significance \(\alpha=0.05\), sample sizes from 8 to 16 and variance ratios from 1 to 2. Analogous results are presented for resampling modifications of the Wilcoxon two-sample tests under the heteroscedastic null hypothesis.

MSC:

62G10 Nonparametric hypothesis testing
62G09 Nonparametric statistical resampling methods
65C05 Monte Carlo methods
62F03 Parametric hypothesis testing
62F40 Bootstrap, jackknife and other resampling methods
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