Abstract
In this research we propose several nonparametric simultaneous test procedures for location and scale parameters. We construct test statistics based on linear rank statistics choosing a suitable combining function. We obtain the overall p -values by applying the permutation principle. We compare the efficiency amongst combining functions by obtaining empirical powers through a simulation study. We discuss some interesting aspects of our procedure as concluding remarks.
Highlights
In order to improve test performance, some nonparametric testing procedures have adopted the trend of using several nonparametric test statistics simultaneously
One may consider reducing the scope of the null hypothesis by splitting it into several sub-null hypotheses according to the interesting aspects of the underlying distribution and intersecting them
Performing some reasonable nonparametric tests for each individual sub-null hypothesis and combining their results with a chosen combining function, one may obtain an overall p-value from the null distribution of the combined test statistic
Summary
In order to improve test performance, some nonparametric testing procedures have adopted the trend of using several nonparametric test statistics simultaneously. Simultaneous use of several nonparametric tests can be applied to the problem of testing location-scale parameters concurrently, for the two-sample case. Performing some reasonable nonparametric tests for each individual sub-null hypothesis and combining their results with a chosen combining function, one may obtain an overall p-value from the null distribution of the combined test statistic. This can be called a nonparametric simultaneous test procedure for the locationscale problem.
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