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

2016/10/29 by Eugenia Stoimenova, N. Balakrishnan, Stoimenova, Eugenia +1 · 1 citation
Decision Sciences · Mathematics · #62E15 #62G10 #Advanced Statistical Process Monitoring #FOS: Mathematics #Probability and Risk Models #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1610.09502

openalex publication_date 2016/10/29 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

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 Šidák'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.

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