On locally most powerful sequential rank tests. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Kalina, Jan
• Is Part Of: Sequential analysis. Volume 36:Issue 1(2017)
• Page Start: 111
• Page End: 125
• Publication Date: 2017-01-02
• Subjects: Nonparametric tests -- sequential ranks -- stopping variable; 62G10 -- 62G30 -- 62L10; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2016.1275501
• Languages: English
• ISSNs: 0747-4946

Abstract

ABSTRACT: Sequential ranks are defined as ranks of such observations, which have been observed so far in a sequential design. This article studies hypotheses tests based on sequential ranks for different situations. The locally most powerful sequential rank test is derived for the hypothesis of randomness against a general alternative, including the two-sample difference in location or regression in location as special cases for the alternative hypothesis. Further, the locally most powerful sequential rank tests are derived for the one-sample problem and for independence of two samples in an analogous spirit as the classical results of Hájek and Šidák (1967 ) for (classical) ranks. The locally most powerful tests are derived for a fixed sample size and the results bring arguments in favor of existing tests. In addition, we propose a sequential testing procedure based on these statistics of the locally most powerful tests. Principles of such sequential testing are explained on the two-sample Wilcoxon test based on sequential ranks.