Dominance refinements of the Smirnov two-sample test

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    Abstract

    We prove the following conjecture of Narayana: there are no nontrivial dominance refinements of the Smirnov two-sample test if and only if the two sample sizes are relatively prime. We also count the number of natural significance levels of the Smirnov two-sample test in terms of the sample sizes and relate this to the Narayana conjecture. In particular, Smirnov tests with relatively prime sample sizes turn out to have many more natural significance levels than do Smirnov tests whose sample sizes are not relatively prime (for example, equal sample sizes).
    Original languageEnglish
    Pages (from-to)51-60
    Number of pages10
    JournalJournal of Statistical Planning and Inference
    Volume66
    Issue number1
    DOIs
    Publication statusPublished - 1998

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