Sidak-type tests for the two-sample problem based on precedence and exceedance statistics

TL;DR

This paper introduces nonparametric two-sample tests based on precedence and exceedance statistics, extending Sidak's test, with exact null distributions, large-sample approximations, and power analysis against Lehmann alternatives.

Contribution

It proposes new nonparametric tests for ordered alternatives based on precedence and exceedance, including their exact distributions and power properties, extending Sidak's test framework.

Findings

Exact null distributions derived for the proposed tests.

Large-sample approximations discussed for practical use.

Power analysis shows effectiveness against Lehmann alternatives.

Abstract

This paper deals with a class of nonparametric two-sample tests for ordered alternatives. The test statistics proposed are based on the number of observations from one sample that precede or exceed a threshold specified by the other sample, and they are extensions of \v{S}id\'ak's test. We derive their exact null distributions and also discuss a large-sample approximation. We then study their power properties exactly against the Lehmann alternative and make some comparative comments. Finally, we present an example to illustrate the proposed tests.