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Monotonicity of Rank Statistics in some Non–parametric: Testing Problems

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  • B.F. Schriever

Abstract

For some non–parametric testing problems (one–sided two–sample problem, k–sample trend problem, testing independence against positive dependence) a partial ordering, denoted by ≥, over the alternatives is defined. This partial ordering expresses the strength of the deviation from the null–hypothesis. All familiar rank tests turn out to become more powerful under “increasing” alternatives; that is, all familiar rank statistics preserve the ordering stochastically in samples whenever it is present between underlying distributions. As a tool, the sample equivalence of ≥ is introduced as a partial ordering over pairs of permutations. Functions, defined on pairs of permutations, which preserve this ordering are studied.

Suggested Citation

  • B.F. Schriever, 1987. "Monotonicity of Rank Statistics in some Non–parametric: Testing Problems," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 41(2), pages 99-109, June.
    • Handle: RePEc:bla:stanee:v:41:y:1987:i:2:p:99-109
    DOI: 10.1111/j.1467-9574.1987.tb01176.x
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    Cited by:

    1. B. Monjardet, 1997. "Concordance between two linear orders: The Spearman and Kendall coefficients revisited," Journal of Classification, Springer;The Classification Society, vol. 14(2), pages 269-295, September.

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