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June, 1991 Note on the Tail Behavior of General Weighted Empirical Processes
Martien C. A. van Zuijlen
Ann. Statist. 19(2): 1102-1105 (June, 1991). DOI: 10.1214/aos/1176348143


Under minimal conditions precise bounds are obtained for the expectation of the supremum of the weighted empirical process over the interval $(0, 1/(n(\log n)^{d - 1}))$, where $d$ is the dimension of the underlying random vectors. The allowed growth of the weight function is optimal in the iid case. The results will have broad applications in the theory of all kinds of nonstandard weighted empirical processes, such as empirical processes based on uniform spacings or $U$-statistics, where it is often not so easy to show directly (as in the iid case) that the considered suprema converge to 0 in probability.


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Martien C. A. van Zuijlen. "Note on the Tail Behavior of General Weighted Empirical Processes." Ann. Statist. 19 (2) 1102 - 1105, June, 1991.


Published: June, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0725.62047
MathSciNet: MR1105867
Digital Object Identifier: 10.1214/aos/1176348143

Primary: 62E20
Secondary: 62G99 , 62H10

Keywords: tail behavior , weighted empirical processes

Rights: Copyright © 1991 Institute of Mathematical Statistics


Vol.19 • No. 2 • June, 1991
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