A test for bivariate two sample location problem

Kanwar Sen, Sunil Kumar Mathur

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

A consistent test for difference in locations between two bivariate populations is proposed. The test is similar as the Mann-Whitney test and depends on the exceedances of slopes of the two samples where slope for each sample observation is computed by taking the ratios of the observed values. In terms of the slopes, it reduces to a univariate problem. The power of the test has been compared with those of various existing tests by simulation. The proposed test statistic is compared with Mardia's(1967) test statistics, Peters-Randies (1991) test statistic, Wilcoxon's rank sum test statistic and Hotelling's T2 test statistic using Monte Carlo technique. It performs better than other statistics compared for small differences in locations between two populations when underlying population is population 7(light tailed population) and sample sizes are 15 and 18 respectively. When underlying population is population 6(heavy tailed population) and sample sizes are 15 and 18 it performs better than other statistics compared except Wilcoxon's rank sum test statistic for small differences in location between two populations. It performs better than Mardia's(1967) test statistic for large differences in location between two populations when underlying population is bivariate normal mixture with probability P=0.5, population 6, Pearson type II population and Pearson type VII population for sample sizes 15 and 18. Under bivariate normal population it performs as good as Mardia's (1967) test statistic for small differences in locations between two populations and sample sizes 15 and 18. For sample sizes 25 and 28 respectively it performs better than Mardia's (1967) test statistic when underlying population is population 6, Pearson type II population and Pearson type VII population.

Original languageEnglish (US)
Pages (from-to)417-436
Number of pages20
JournalCommunications in Statistics - Theory and Methods
Volume29
Issue number2
StatePublished - Feb 1 2000

Fingerprint

Two-sample Problem
Location Problem
Statistics
Test Statistic
Sample Size
Population Size
Wilcoxon rank-sum test
Bivariate Normal
Slope
Mann-Whitney test
Consistent Test
Hotelling's T2
Normal Mixture
Exceedance
Normal Population
Monte Carlo Techniques

Keywords

  • Bivariate population
  • Consistent
  • Power

ASJC Scopus subject areas

  • Statistics and Probability
  • Safety, Risk, Reliability and Quality

Cite this

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

In: Communications in Statistics - Theory and Methods, Vol. 29, No. 2, 01.02.2000, p. 417-436.

Research output: Contribution to journalArticle

Sen, Kanwar ; Mathur, Sunil Kumar. / A test for bivariate two sample location problem. In: Communications in Statistics - Theory and Methods. 2000 ; Vol. 29, No. 2. pp. 417-436.
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