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June, 1951 Consistency and Unbiasedness of Certain Nonparametric Tests
E. L. Lehmann
Ann. Math. Statist. 22(2): 165-179 (June, 1951). DOI: 10.1214/aoms/1177729639


It is shown that there exist strictly unbiased and consistent tests for the univariate and multivariate two- and $k$-sample problem, for the hypothesis of independence, and for the hypothesis of symmetry with respect to a given point. Certain new tests for the univariate two-sample problem are discussed. The large sample power of these tests and of the Mann-Whitney test are obtained by means of a theorem of Hoeffding. There is a discussion of the problem of tied observations.


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E. L. Lehmann. "Consistency and Unbiasedness of Certain Nonparametric Tests." Ann. Math. Statist. 22 (2) 165 - 179, June, 1951.


Published: June, 1951
First available in Project Euclid: 28 April 2007

zbMATH: 0045.40903
MathSciNet: MR40632
Digital Object Identifier: 10.1214/aoms/1177729639

Rights: Copyright © 1951 Institute of Mathematical Statistics

Vol.22 • No. 2 • June, 1951
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