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2014 Precise Asymptotics on Second-Order Complete Moment Convergence of Uniform Empirical Process
Junshan Xie, Lin He
Abstr. Appl. Anal. 2014: 1-5 (2014). DOI: 10.1155/2014/143581

Abstract

Let {ξi,1in} be a sequence of iid U[0, 1]-distributed random variables, and define the uniform empirical process Fn(t)=n-1/2i=1n(I{ξit}-t),0t1, Fn=sup0t1|Fn(t)|. When the nonnegative function g(x) satisfies some regular monotone conditions, it proves that limϵ01/-logϵn=1g(n)/g(n)E{Fn2I{Fnϵg(n)}}=π2/6.

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Junshan Xie. Lin He. "Precise Asymptotics on Second-Order Complete Moment Convergence of Uniform Empirical Process." Abstr. Appl. Anal. 2014 1 - 5, 2014. https://doi.org/10.1155/2014/143581

Information

Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07021803
MathSciNet: MR3256238
Digital Object Identifier: 10.1155/2014/143581

Rights: Copyright © 2014 Hindawi

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