The law of the iterated logarithm and central limit theorem for L-statistics

JOURNAL OF MULTIVARIATE ANALYSIS

卷:78

Article

Li, D ; Rao, MB ; Tomkins, RJ

关键词: central limit theorem;    empirical process;    laws of the iterated logarithm;    L-statistics;    strong law of large numbers;   

DOI  :  10.1006/jmva.2000.1954

来源: Elsevier

【 摘 要 】

The Chung-Smirnov law of the iterated logarithm and the Finkelstein functional law of the iterated logarithm for empirical processes are used to establish new results on the central limit theorem, the law of the iterated logarithm, and the strong law of largo numbers for L-statistics with certain bounded and smooth weight functions. These results are used to obtain necessary and sufficient conditions for almost sure convergence and for convergence in distribution of some well-known L-statistics and U-statistics, including Gini's mean difference statistic. A law of the logarithm for weighted sums of order statistics is also presented. (C) 2001 Academic Press.

【 授权许可】

Free