A Generalization of the Rank Transform in the Two-Sample Location Problem

Ravinder Nath, B. S. Duran

Research output: Contribution to journalArticle

Abstract

The t-statistic computed as a function of the scores of a two-sampie linear rank statistic, rather than the observations them-selves, yields a statistic TCR which can be used to test for the equality of locations of two populations. For the Wilcoxon scores, the statistic TcR reduces to the f, rank transform” statistic T. By assuming the appropriate regularity conditions on the scores, TCR is shown to have approximately a t-distribution. The asymptotic relative efficiency (ARE) of T is the same as that of the corre-CR sponding linear rank statistic. The robustness of TCR, with respect to significance level and power, is studied by Monte Carlo simulation when the distributions are normal, uniform, double exponential Cauchy, and exponential.

Original languageEnglish
Pages (from-to)1437-1455
Number of pages19
JournalCommunications in Statistics - Theory and Methods
Volume10
Issue number14
DOIs
StatePublished - Jan 1 1981
Externally publishedYes

Fingerprint

Two-sample Problem
Location Problem
Statistic
Linear Rank Statistics
Transform
Asymptotic Relative Efficiency
t-distribution
Significance level
Regularity Conditions
Cauchy
Equality
Monte Carlo Simulation
Robustness
Generalization

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Cite this

A Generalization of the Rank Transform in the Two-Sample Location Problem. / Nath, Ravinder; Duran, B. S.

In: Communications in Statistics - Theory and Methods, Vol. 10, No. 14, 01.01.1981, p. 1437-1455.

Research output: Contribution to journalArticle

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