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2017•arXiv (Cornell University)Open access

Smoothed nonparametric two-sample tests

Taku Moriyama, Yoshihiko Maesono

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Abstract

We propose new smoothed median and the Wilcoxon's rank sum test. As is pointed out by Maesono et al.(2016), some nonparametric discrete tests have a problem with their significance probability. Because of this problem, the selection of the median and the Wilcoxon's test can be biased too, however, we show new smoothed tests are free from the problem. Significance probabilities and local asymptotic powers of the new tests are studied, and we show that they inherit good properties of the discrete tests.

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What this paper is about

We propose new smoothed median and the Wilcoxon's rank sum test. As is pointed out by Maesono et al.(2016), some nonparametric discrete tests have a problem with their significance probability. Because of this problem, the selection of the median and the Wilcoxon's test can be biased too, however, we show new smoothed tests are free from the problem. Significance probabilities and local asymptotic powers of the new tests are studied, and we show that they inherit good properties of the discrete tests.

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Available abstract

We propose new smoothed median and the Wilcoxon's rank sum test. As is pointed out by Maesono et al.(2016), some nonparametric discrete tests have a problem with their significance probability. Because of this problem, the selection of the median and the Wilcoxon's test can be biased too, however, we show new smoothed tests are free from the problem. Significance probabilities and local asymptotic powers of the new tests are studied, and we show that they inherit good properties of the discrete tests.

Key concepts: Wilcoxon signed-rank test, Nonparametric statistics, Mathematics, Selection (genetic algorithm), Statistical hypothesis testing, Statistics, Rank (graph theory), Computer science

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