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January, 1974 The Invariance Principle for One-Sample Rank-Order Statistics
Pranab Kumar Sen
Ann. Statist. 2(1): 49-62 (January, 1974). DOI: 10.1214/aos/1176342612

Abstract

Analogous to the Donsker theorem on partial cumulative sums of independent random variables, for a broad class of one-sample rank order statistics, weak convergence to Brownian motion processes is studied here. A simple proof of the asymptotic normality of these statistics for random sample sizes is also presented. Some asymptotic results on renewal theory for one-sample rank order statistics are derived.

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Pranab Kumar Sen. "The Invariance Principle for One-Sample Rank-Order Statistics." Ann. Statist. 2 (1) 49 - 62, January, 1974. https://doi.org/10.1214/aos/1176342612

Information

Published: January, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0273.60005
MathSciNet: MR345309
Digital Object Identifier: 10.1214/aos/1176342612

Subjects:
Primary: 60B10
Secondary: 62G99

Keywords: Brownian motion processes , Invariance principles , Martingales , one-sample rank order statistics , random sample sizes , renewal theory , weak convergence

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 1 • January, 1974
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