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February, 1968 On a Further Robustness Property of the Test and Estimator Based on Wilcoxon's Signed Rank Statistic
Pranab Kumar Sen
Ann. Math. Statist. 39(1): 282-285 (February, 1968). DOI: 10.1214/aoms/1177698535

Abstract

The robust-efficiency of the test and estimator based on Wilcoxon's [7] signed rank statistic when the sample observations are drawn from different populations is studied here. Let $X_1, \cdots, X_n$ be $n$ independent random variables distributed according to continuous cumulative distribution functions (cdf) $F_1(x), \cdots, F_n(x)$, respectively. Let $\mathscr{F}$ be the class of all continuous cdf's which are symmetric about their medians. If $F_1 = \cdots = F_n = F \varepsilon \mathscr{F}$, the Wilcoxon's [7] signed rank statistic provides a robust test for and estimator of the median of $F(x)$, (cf. [2], [4], [6], [7]). The asymptotic relative efficiency (ARE) of this test and estimator has been studied by Hodges and Lehmann [1]. The present investigation is concerned with the study of the robust-efficiency of the same when $F_1, \cdots, F_n$ are not necessarily identical.

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Pranab Kumar Sen. "On a Further Robustness Property of the Test and Estimator Based on Wilcoxon's Signed Rank Statistic." Ann. Math. Statist. 39 (1) 282 - 285, February, 1968. https://doi.org/10.1214/aoms/1177698535

Information

Published: February, 1968
First available in Project Euclid: 27 April 2007

zbMATH: 0162.21904
MathSciNet: MR221697
Digital Object Identifier: 10.1214/aoms/1177698535

Rights: Copyright © 1968 Institute of Mathematical Statistics

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Vol.39 • No. 1 • February, 1968
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