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January, 1976 Asymptotic Comparison of Rank Tests for the Regression Problem When Ties are Present
Konrad Behnen
Ann. Statist. 4(1): 157-174 (January, 1976). DOI: 10.1214/aos/1176343351


Without assumptions on the underlying distributions we prove the asymptotic normality of averaged scores rank statistics under all product distributions which are contiguous to the null hypothesis, and find a very simple form of the centering constants. In the one-sided two-sample and trend situations this enables us to show that monotonicity of the scores generating function is equivalent to the asymptotic unbiasedness of the corresponding averaged scores rank test. For such asymptotically unbiased tests we prove simple necessary and sufficient conditions for having bounds for their asymptotic relative efficiency under all contiguous alternatives of the model. As a by-product, we get the local asymptotic superiority of averaged scores rank tests to the associated tests with randomized ranks not only for shift but for general alternatives. In addition we prove that every one-sided averaged scores rank test is asymptotically most powerful (asymptotically equivalent to likelihood ratio test) for a suitable nonparametric subclass of alternatives, provided the test and the associated subclass of alternatives are generated by a nondecreasing, square-integrable function defined on the unit interval.


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Konrad Behnen. "Asymptotic Comparison of Rank Tests for the Regression Problem When Ties are Present." Ann. Statist. 4 (1) 157 - 174, January, 1976.


Published: January, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0321.62048
MathSciNet: MR443206
Digital Object Identifier: 10.1214/aos/1176343351

Primary: 62G10
Secondary: 62E20 , 62G20

Keywords: asymptotic normality , asymptotic optimality , Asymptotic relative efficiency , averaged scores , contiguity , efficiency bounds , Linear rank statistics , randomized ranks , treatment of ties

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 1 • January, 1976
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