A Bahadur efficiency comparison between one and two sample rank statistics and their sequential rank statistic analogues
type: Item
instance of: scholarly article
title: A Bahadur efficiency comparison between one and two sample rank statistics and their sequential rank statistic analogues
zbMATH Open document ID: 0535.62043
DOI: 10.1016/0047-259X(84)90004-6
author: David M. Mason
published in: Journal of Multivariate Analysis
publication date: 1984-01-01T00:00:00Z
review text: Let \(Z_ 1,Z_ 2,..\). be a sequence of i.i.d. random variables and \(R_{in}\) the rank of \(Z_ i\) among \(Z_ 1,...,Z_ n\). Let further \(J_ n(i/(n+1))\) be scores, \(c_{in}\) given regression numbers and \(\bar c_{in}=\sum^{i-1}_{j=1}c_{jn}/(i-1)\). The author compares statistical properties of the test statistic \(T_ n=\sum^{n}_{i=1}c_{in}J_ n(R_{in}/(n+1))\) and its sequential analogue \(M_ n=\sum^{n}_{i=1}(c_{in}-\bar c_{in})J_ i(R_{ii}/(i+1)).\) It is known from the author's paper in Ann. Stat. 9, 424-436 (1981; Zbl 0459.62015) that both statistics have the same Pitman efficiency against local alternatives. The main result of this paper is that in the Bahadur sense both statistics show different efficiency properties. A similar result is established for signed-rank procedures.
Mathematics Subject Classification ID: 62G20
Mathematics Subject Classification ID: 62L10
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 62G10
zbMATH DE Number: 3850295
zbMATH Keywords: Bahadur efficiency comparison
zbMATH Keywords: one and two sample rank statistics
zbMATH Keywords: sequential rank statistic analogues
zbMATH Keywords: laws of large numbers
zbMATH Keywords: Pitman efficiency against local alternatives
zbMATH Keywords: signed-rank procedures
MaRDI profile type: Publication
cites work: Rates of Convergence of Estimates and Test Statistics
cites work: Q5671986
cites work: On the Limit Behaviour of Extreme Order Statistics
cites work: A nonparametric control chart for detecting small disorders
cites work: Q3268650
cites work: Q4114551
cites work: Q5543905
cites work: Asymptotic sufficiency of the vector of ranks in the Bahadur sense
cites work: Q4127195
cites work: Asymptotically Optimal Tests for Multinomial Distributions
cites work: Alternative Efficiencies for Signed Rank Tests
cites work: Q4147508
cites work: Q4749041
cites work: A curious converse of Siever's theorem
cites work: On the use of a statistic based on sequential ranks to prove limit theorems for simple linear rank statistics
cites work: A theorem about probabilities of large deviations with an application to queuing theory
cites work: Q5514924
cites work: A sequential signed-rank test for symmetry
cites work: Q3215459
cites work: On Some Convergence Properties of One-Sample Rank Order Statistics
cites work: Invariance principles for rank discounted partial sums and averages
cites work: On the Probability of Large Deviations and Exact Slopes
cites work: Estimates of location: a large deviation comparison
cites work: An Analogue, for Signed Rank Statistics, of Jureckova's Asymptotic Linearity Theorem for Rank Statistics
cites work: A condition under which the Pitman and Bahadur approaches to efficiency coincide
cites work: Large Deviations and Bahadur Efficiency of Linear Rank Statistics
full work available at URL: 0047-259x(84)90004-6
OpenAlex ID: W1988574516
description: scientific article; zbMATH DE number 3850295