The Annals of Mathematical Statistics

Asymptotic Optimality and ARE of Certain Rank-Order Tests under Contiguity

Konrad Behnen

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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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Ann. Math. Statist., Volume 42, Number 1 (1971), 325-329.

First available in Project Euclid: 27 April 2007

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Behnen, Konrad. Asymptotic Optimality and ARE of Certain Rank-Order Tests under Contiguity. Ann. Math. Statist. 42 (1971), no. 1, 325--329. doi:10.1214/aoms/1177693515.

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