On locally most powerful sequential rank tests

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.

KEYWORDS:

• Nonparametric tests
• sequential ranks
• stopping variable

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G10
• 62G30
• 62L10

Acknowledgments

The author would like to thank Jana Jurečková, the anonymous referees, an associate editor, and the editor-in-chief for their time and constructive advice.