The Functional Law of the Iterated Logarithm for the Empirical Process Based on Sample Means期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

The Functional Law of the Iterated Logarithm for the Empirical Process Based on Sample Means

Authors:	John H. J. Einmahl Andrew Rosalsky

Affiliation:	(1) EURANDOM and Department of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;(2) Department of Statistics, University of Florida, Box 118545, Gainesville, Florida, 32611-8545, U.S.A.

Abstract:	Consider a double array $left{ {X_{i,j} ;i geqslant 1,j geqslant } right}$ of i.i.d. random variables with mean and variance and set $Z_{i,n} = n^{ - 1/2} sumnolimits_{j = 1}^n {(X_{i,j} - mu )} /sigma$ . Let $hat Phi _{N,n}$ denote the empirical distribution function of Z_{1, n},..., Z_{N, n} and let be the standard normal distribution function. The main result establishes a functional law of the iterated logarithm for $sqrt N (hat Phi _{N,n} - Phi )$ , where n=n(N) as N. For the proof, some lemmas are derived which may be of independent interest. Some corollaries of the main result are also presented.

Keywords:	empirical process based on sample means functional law of the iterated logarithm double array relative compactness central limit theorem Berry– Esseen inequality
本文献已被 SpringerLink 等数据库收录！