Open Access
May, 1976 Weak Convergence of Sequential Linear Rank Statistics
Henry I. Braun
Ann. Statist. 4(3): 554-575 (May, 1976). DOI: 10.1214/aos/1176343461


A sequential version of Chernoff-Savage linear rank statistics is introduced as a basis for inference. The principal result is an invariance principle for two-sample rank statistics, i.e., under a fixed alternative the sequence of sequential linear rank statistics converges weakly to a Wiener process. The domain of application of the theorem is quite broad and includes score functions which tend to infinity at the end points much more rapidly than that of the normal scores test. The method of proof involves new results in the theory of multiparameter empirical processes as well as some new probability bounds on the joint behavior of uniform order statistics. Applications of weak convergence are explored; in particular, the extension of the theory of Pitman efficiency to the sequential case.


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Henry I. Braun. "Weak Convergence of Sequential Linear Rank Statistics." Ann. Statist. 4 (3) 554 - 575, May, 1976.


Published: May, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0331.62017
MathSciNet: MR403017
Digital Object Identifier: 10.1214/aos/1176343461

Primary: 62E20
Secondary: 62G10 , 62G20 , 62L10

Keywords: Asymptotic efficiency , Sequential linear rank statistics , Uniform order statistics , weak convergence

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 3 • May, 1976
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