A class of \v{S}id\'ak-type tests based on maximal precedence and exceedance statistic

TL;DR

This paper introduces a new nonparametric two-sample test combining maximal precedence and exceedance statistics, suitable for two-sided alternatives, with exact distribution and demonstrated effectiveness.

Contribution

It develops a novel two-sided nonparametric test based on precedence and exceedance, extending existing methods and providing exact distribution under null and Lehmann alternatives.

Findings

The proposed test has competitive power compared to existing precedence-exceedance tests.

Exact distribution formulas are derived for null and Lehmann alternatives.

Real-life data example demonstrates practical applicability.

Abstract

A class of nonparametric two-sample tests has been proposed in this article. As a generalization of the original \v{S}id\'aks' test, the proposed test statistic is developed as the sum of the maximal precedence and maximal exceedance statistics. Unlike the \v{S}id\'ak-type precedence-exceedance test and the maximal precedence test, the proposed test is suitable for a two-sided alternative while being free from any parametric assumption. Exact distribution of the test statistic is obtained under the null as well as under the Lehmann alternative. Power value comparison has been carried out that shows the competency of the proposed test as a useful alternative to a number of existing tests based on precedence-exceedance statistics. Real-life example is provided to illustrate the application of the proposed test.