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Dominance refinements of the Smirnov two-sample test

✍ Scribed by A. Di Bucchianico; D.E. Loeb

Book ID: 104340456
Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 462 KB
Volume: 66
Category: Article
ISSN: 0378-3758
DOI: 10.1016/s0378-3758(97)00081-5

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✦ Synopsis

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, Smimov 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).

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