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November, 1973 A Class of Non-Parametric Tests for Homogeneity Against Ordered Alternatives
Peter V. Tryon, Thomas P. Hettmansperger
Ann. Statist. 1(6): 1061-1070 (November, 1973). DOI: 10.1214/aos/1176342557


In this paper, the $c$-sample location problem with ordered or restricted alternatives is considered. Linear combinations of Chernoff-Savage type two-sample statistics computed among the $c(c - 1)/2$ pairs of samples are proposed as test statistics. It is shown that for each linear combination of two-sample statistics there is another linear combination, using only the $c - 1$ two-sample statistics based on adjacent samples as determined by the alternative, which has the same Pitman efficacy. If the ordered alternative is restricted further by specifying the relative spacings in the alternative, then the weighting coefficients can be chosen to maximize the Pitman efficacy over the class of linear combinations. It is also shown that the statistics proposed by Jonkheere [4] and Puri [9] have maximum Pitman efficacy when the alternative specifies equal spacings.


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Peter V. Tryon. Thomas P. Hettmansperger. "A Class of Non-Parametric Tests for Homogeneity Against Ordered Alternatives." Ann. Statist. 1 (6) 1061 - 1070, November, 1973.


Published: November, 1973
First available in Project Euclid: 12 April 2007

zbMATH: 0275.62041
MathSciNet: MR353560
Digital Object Identifier: 10.1214/aos/1176342557

Keywords: equally spaced alternatives , linear combinations of two-sample rank tests , Tests for ordered alternatives

Rights: Copyright © 1973 Institute of Mathematical Statistics


Vol.1 • No. 6 • November, 1973
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