On the limiting Pitman efficiency of some rank tests of independence
type: Item
instance of: scholarly article
title: On the limiting Pitman efficiency of some rank tests of independence
zbMATH Open document ID: 0615.62053
DOI: 10.1016/0047-259X(86)90082-5
author: Teresa Ledwina
published in: Journal of Multivariate Analysis
publication date: 1986-01-01T00:00:00Z
review text: Kendall's tau and Spearman's rho may be expressed by the use of standard sequences with parameter \(a=1\). The paper uses the fact that the main assumption of \textit{H. S. Wieand}'s theorem [Ann. Stat. 4, 1003-1011 (1976; Zbl 0351.62033)] may be replaced by an equivalent one which is presented in section 2. Taking \(R_ i(S_ i)\) as the rank of \(X_ i(Y_ i)\) and I(A) as the indicator of the set A, the statistic \[ t_ n=\sup_{0<p<1}(12n)^{1/2}(\sum^{n}_{i=1}(R_ i/n)(p-I(S_ i\leq np))/n) \] is also usable for testing independence and it is a standard sequence with \(a=4\). Section 3 is devoted to prove that \(t_ n\) fulfills the equivalent condition as Kendall's tau and Spearman's rho do. Then the well known theorem of \textit{J. Kiefer} and \textit{J. Wolfowitz} [Trans. Am. Math. Soc. 87, 173-186 (1958; Zbl 0088.113)] is satisfied. Some examples of the limiting Pitman efficiency of the statistics studied are derived in Section 4.
Mathematics Subject Classification ID: 62G20
Mathematics Subject Classification ID: 62H15
Mathematics Subject Classification ID: 62G10
zbMATH DE Number: 3996880
zbMATH Keywords: positive quadrant dependence
zbMATH Keywords: rank tests
zbMATH Keywords: Bahadur efficiency
zbMATH Keywords: Wieand's theorem
zbMATH Keywords: Kiefer-Wolfowitz theorem
zbMATH Keywords: testing independence
zbMATH Keywords: standard sequence
zbMATH Keywords: Kendall's tau
zbMATH Keywords: Spearman's rho
zbMATH Keywords: limiting Pitman efficiency
reviewed by: Carlos Narciso Bouza Herrera
MaRDI profile type: Publication
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full work available at URL: 0047-259x(86)90082-5
OpenAlex ID: W2048578891
description: scientific article; zbMATH DE number 3996880