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

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 ofŠidák'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.

A consistent statistical test based on bivariate random samples

“…There are many interesting recent papers in statistical literature related to equality of two probability distributions, see, e.g., [1,[23][24][25]. Jiménez-Gamero et al [15] proposed a test for testing equality of distribution of two samples based on empirical characteristic functions.…”

On precedence tests with double sampling

“…This test was first introduced by Nelson (1963). Then several authors have considered the precedence-type statistics in online monitoring and retrospective testing problems; e.g., Ilbott and Nadler (1965), Shorack (1967), Nelson (1993), Chakraborti and Van der Laan (1996), van der Laan and Chakraborti (2001), Balakrishnan and Frattina (2000), Balakrishnan (2004, 2005), Balakrishnan et al (2008), Balakrishnan et al (2010), Ng et al 2 (2013), Balakrishnan et al (2015b), Balakrishnan et al (2015a), Stoimenova and Balakrishnan (2017), Chakraborty et al (2018), Chakraborty et al (2022), to name a few. For instance, Ng and Balakrishnan (2005) have proposed the weighted precedence test and the weighted maximal precedence test as extensions to the precedence test (Nelson (1963)) and maximal precedence test (Balakrishnan and Frattina (2000)).…”