A combined bootstrap test for the two-sample location problem

The comparison of two samples is a problem very frequently encountered in practice. There is active interest in researching for tests that are powerful also when the data are not compatible with the assumptions of normality and equal variances–as it is common in many fields–while controlling their type-one error rate. The Yuen test is a familiar method based on trimmed means. There is no agreement in the literature about the preferable rate of trimming. This paper has two aims: to study the power of many Yuen tests with different trimming rates and propose a bootstrap test based on the combination of Yuen tests with different trimming rates. It is shown that the various Yuen tests have very different power for different distributions because the best rate of trimming depends on distribution tailweight. Conversely, the combined test is powerful irrespective to the underlying distribution.