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313838

Two-Sample Nonparametric Test of Homogeneity

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Last updated: 28 Dec 2024

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Abstract

Given independent multivariate random samples x1, x2, ..., xnand y1, y2….yn   from distributions F and G, a test is desired for Ho: F = G against general alternatives. Consider the k (n + n2) possible ways of choosing one observation from the combined samples and then one of its k nearest neighbors, and let Sk be the proportion of these choices in which the point and neighbor are in the came sample. SCHILLING (1986) proposed Sk  as a test statistic, but did not indicate how to determine k. BARAKAT, QUADE, and SALAMA (1996) proposed a test statistic W=1 kSk, which is equivalent to a sum of N Wilkoxon rank sums. The limiting distribution of the test was not found yet. We suggest as a test statistic TM=ΣΣ h(m,j), Where h (m,j) = I{Jth nearest neighbor of the median m is a y}.   

DOI

10.21608/esju.2000.313838

Keywords

Multivariate Random Samples, BARAKAT - QUADE, SALAMA - Wilkoxon Rank

Volume

44

Article Issue

2

Related Issue

43032

Issue Date

2000-12-01

Publish Date

2000-12-01

Page Start

250

Page End

262

Print ISSN

0542-1748

Online ISSN

2786-0086

Link

https://esju.journals.ekb.eg/article_313838.html

Detail API

https://esju.journals.ekb.eg/service?article_code=313838

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10

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Original Article

Type Code

1,914

Publication Type

Journal

Publication Title

The Egyptian Statistical Journal

Publication Link

https://esju.journals.ekb.eg/

MainTitle

Two-Sample Nonparametric Test of Homogeneity

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Article

Created At

28 Dec 2024