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Distribution-Free Tests for Hypothesis Testing in Nonparametric Families

Abstract

For hypothesis testing in a nonparametric family, the null distribution of test statistics must be the same for all distributions in the subfamily satisfying the null hypothesis so as to choose a critical region at a given level of significance. Such tests are called distribution-free tests. Since ranks and empirical distribution functions (edf) have the distribution-free property, such tests would be based on ranks and edf. After presenting the main properties of ranks and order statistics, rank tests for some basic hypothesis testing problems are introduced and their asymptotic distributions are derived, representing them as U-statistics and using Hájek ...

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