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January, 1973 Convergence of Reduced Empirical and Quantile Processes with Application to Functions of Order Statistics in the Non-I.I.D. Case
Galen R. Shorack
Ann. Statist. 1(1): 146-152 (January, 1973). DOI: 10.1214/aos/1193342391

Abstract

Any triangular array of row independent $\mathrm{rv}$'s having continuous $\mathrm{df}$'s can be transformed naturally so that the empirical and quantile processes of the resulting $\mathrm{rv}$'s are relatively compact. Moreover, convergence (to a necessarily normal process) takes place if and only if a simple covariance function converges pointwise. Using these results we derive the asymptotic normality of linear combinations of functions of order statistics of non-i.i.d. $\mathrm{rv}$'s in the case of bounded scores.

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Galen R. Shorack. "Convergence of Reduced Empirical and Quantile Processes with Application to Functions of Order Statistics in the Non-I.I.D. Case." Ann. Statist. 1 (1) 146 - 152, January, 1973. https://doi.org/10.1214/aos/1193342391

Information

Published: January, 1973
First available in Project Euclid: 25 October 2007

zbMATH: 0255.62044
MathSciNet: MR336776
Digital Object Identifier: 10.1214/aos/1193342391

Subjects:
Primary: 62G30
Secondary: 60B10, 62E20

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 1 • January, 1973
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