A bivariate signed rank test for two sample location problem

Kanwar Sen, Sunil Mathur

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

An affine-invariant signed rank test for the difference in location between two symmetric populations is proposed. The proposed test statistic is compared with Hotelling's T2 test statistic, Mardia's(1967)test statistic, Peters-Randles(1991) test statistic and Wilcoxon's rank sum test statistic using a Monte Carlo Study. It performs better than Mardia's test statistic under almost all populations considered. Under the bivariate normal distribution, it performs better than other test statistics compared for small differences in location between two populations except Hotelling's T2. It performs better than all statistics, including Hotelling's T2, for sample size 15 when samples are drawn from Pearson type II, Pearson type VII, bivariate normal mixtures and populations 6 and 7 for small differences in location between the two populations. For heavy tailed population 6, the proposed test statistic performs as good as Hotelling's T2 and Wilcoxon's test statistic for sample size 25. A Huber type Robust version ( see for example, Huber(1977)) of the proposed test statistic is also found useful.

Original languageEnglish (US)
Pages (from-to)3031-3050
Number of pages20
JournalCommunications in Statistics - Theory and Methods
Volume26
Issue number12
DOIs
StatePublished - Jan 1 1997

Fingerprint

Two-sample Problem
Rank Test
Location Problem
Signed
Test Statistic
Hotelling's T2
Sample Size
Wilcoxon rank-sum test
Bivariate Normal
Bivariate Normal Distribution
Wilcoxon Test
Normal Mixture
Affine Invariant
Normal Population
Monte Carlo Study
Statistics

Keywords

  • Affine-invariant
  • Power
  • Robust
  • Symmetric population

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

A bivariate signed rank test for two sample location problem. / Sen, Kanwar; Mathur, Sunil.

In: Communications in Statistics - Theory and Methods, Vol. 26, No. 12, 01.01.1997, p. 3031-3050.

Research output: Contribution to journalArticle

Sen, Kanwar ; Mathur, Sunil. / A bivariate signed rank test for two sample location problem. In: Communications in Statistics - Theory and Methods. 1997 ; Vol. 26, No. 12. pp. 3031-3050.
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