## The Annals of Mathematical Statistics

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

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

#### Abstract

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.

#### Article information

**Source**

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

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177693515

**Digital Object Identifier**

doi:10.1214/aoms/1177693515

**Mathematical Reviews number (MathSciNet)**

MR275593

**Zentralblatt MATH identifier**

0224.62019

**JSTOR**

links.jstor.org

#### Citation

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. https://projecteuclid.org/euclid.aoms/1177693515