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May, 1977 A Law of the Iterated Logarithm for Functions of Order Statistics
Jon A. Wellner
Ann. Statist. 5(3): 481-494 (May, 1977). DOI: 10.1214/aos/1176343845

Abstract

A general law of the iterated logarithm for linear combinations of order statistics is proved. The key tools are (1) iterated logarithm convergence of the uniform empirical process $U_n$ in $\rho_q$-metrics due to B. R. James and (2) almost sure "nearly linear" bounds for the empirical distribution function. A law of the iterated logarithm for the quantile process is also established.

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Jon A. Wellner. "A Law of the Iterated Logarithm for Functions of Order Statistics." Ann. Statist. 5 (3) 481 - 494, May, 1977. https://doi.org/10.1214/aos/1176343845

Information

Published: May, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0365.62046
MathSciNet: MR436297
Digital Object Identifier: 10.1214/aos/1176343845

Subjects:
Primary: 60F15
Secondary: 62G30

Keywords: empirical df , Law of the iterated logarithm , nearly linear bounds , order statistics , quantile process

Rights: Copyright © 1977 Institute of Mathematical Statistics

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Vol.5 • No. 3 • May, 1977
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