## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 39, Number 1 (1968), 282-285.

### On a Further Robustness Property of the Test and Estimator Based on Wilcoxon's Signed Rank Statistic

#### 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.

#### Article information

**Source**

Ann. Math. Statist., Volume 39, Number 1 (1968), 282-285.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177698535

**Digital Object Identifier**

doi:10.1214/aoms/1177698535

**Mathematical Reviews number (MathSciNet)**

MR221697

**Zentralblatt MATH identifier**

0162.21904

**JSTOR**

links.jstor.org

#### Citation

Sen, Pranab Kumar. On a Further Robustness Property of the Test and Estimator Based on Wilcoxon's Signed Rank Statistic. Ann. Math. Statist. 39 (1968), no. 1, 282--285. doi:10.1214/aoms/1177698535. https://projecteuclid.org/euclid.aoms/1177698535