Abstract and Applied Analysis

Precise Asymptotics on Second-Order Complete Moment Convergence of Uniform Empirical Process

Junshan Xie and Lin He

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

Let { ξ i , 1 i n } be a sequence of iid U[0, 1]-distributed random variables, and define the uniform empirical process F n ( t ) = n - 1 / 2 i = 1 n ( I { ξ i t } - t ) , 0 t 1 , F n = s u p 0 t 1 | F n ( t ) | . When the nonnegative function g ( x ) satisfies some regular monotone conditions, it proves that lim ϵ 0 1 / - l o g ϵ n = 1 g ( n ) / g ( n ) E { F n 2 I { F n ϵ g ( n ) } } = π 2 / 6 .

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 143581, 5 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412277171

Digital Object Identifier
doi:10.1155/2014/143581

Mathematical Reviews number (MathSciNet)
MR3256238

Zentralblatt MATH identifier
07021803

Citation

Xie, Junshan; He, Lin. Precise Asymptotics on Second-Order Complete Moment Convergence of Uniform Empirical Process. Abstr. Appl. Anal. 2014 (2014), Article ID 143581, 5 pages. doi:10.1155/2014/143581. https://projecteuclid.org/euclid.aaa/1412277171


Export citation