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July, 1987 A Refinement of the KMT Inequality for the Uniform Empirical Process
David M. Mason, Willem R. Van Zwet
Ann. Probab. 15(3): 871-884 (July, 1987). DOI: 10.1214/aop/1176992070


A refinement of the Komlos, Major and Tusnady (1975) inequality for the supremum distance between the uniform empirical process and a constructed sequence of Brownian bridges is obtained. This inequality leads to a weighted approximation of the uniform empirical and quantile processes by a sequence of Brownian bridges dual to that recently given by M. Csorgo, S. Csorgo, Horvath and Mason (1986). The present theory approximates the uniform empirical process more closely than the uniform quantile process, whereas the former theory more closely approximates the uniform quantile process.


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David M. Mason. Willem R. Van Zwet. "A Refinement of the KMT Inequality for the Uniform Empirical Process." Ann. Probab. 15 (3) 871 - 884, July, 1987.


Published: July, 1987
First available in Project Euclid: 19 April 2007

zbMATH: 0638.60040
MathSciNet: MR893903
Digital Object Identifier: 10.1214/aop/1176992070

Primary: 60F99
Secondary: 60F17

Keywords: Brownian bridge approximation , Weighted empirical and quantile processes

Rights: Copyright © 1987 Institute of Mathematical Statistics


Vol.15 • No. 3 • July, 1987
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