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February, 1971 Asymptotic Optimality and ARE of Certain Rank-Order Tests under Contiguity
Konrad Behnen
Ann. Math. Statist. 42(1): 325-329 (February, 1971). DOI: 10.1214/aoms/1177693515


In this paper we will derive asymptotically optimal rank-order tests for independence against suitable classes of nonparametric alternatives and give asymptotic relative efficiencies (ARE's) of such tests under general contiguous alternatives of positive quadrant dependence (cf. Lehmann [14]). From Lehmann [14] one can also see that such alternatives in some respects are more general than the alternatives considered in Bhuchongkul [1], Konijn [12], Hajek and Sidak [8] page 221), and others. For the problem of symmetry and for the two-sample problem we can get completely analogous results with similar proofs. Details are omitted. The paper is based on the theory of contiguity that was introduced by LeCam [13] and Hajek [6]. The results of this paper complement results obtained by Hodges and Lehmann [9], [10], Chernoff and Savage [3], Hajek [6], van Eeden [4], Bhuchongkul [1], Gokhale [5], and others.


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Konrad Behnen. "Asymptotic Optimality and ARE of Certain Rank-Order Tests under Contiguity." Ann. Math. Statist. 42 (1) 325 - 329, February, 1971.


Published: February, 1971
First available in Project Euclid: 27 April 2007

zbMATH: 0224.62019
MathSciNet: MR275593
Digital Object Identifier: 10.1214/aoms/1177693515

Rights: Copyright © 1971 Institute of Mathematical Statistics

Vol.42 • No. 1 • February, 1971
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