Accession Number : ADA328387
Title : The Law of the Iterated Logarithm and Central Limit Theorem for L-Statistics.
Descriptive Note : Technical rept.,
Corporate Author : PENNSYLVANIA STATE UNIV UNIVERSITY PARK CENTER FOR MULTIVARIATE ANALYSIS
Personal Author(s) : Li, Deli ; Rao, M. B. ; Tomkins, R. J.
PDF Url : ADA328387
Report Date : JUL 1997
Pagination or Media Count : 34
Abstract : The main idea in this paper is that we devise an effective way of combining the Smirnov's law of the iterated logarithm for empirical processes, and some well-known results of limit behavior of L-statistics to establish new results on the central limit theorem, law of the iterated logarithm, and strong law of large numbers, for L-statistics. We show further that this approach can be pursued profitably to obtain necessary and sufficient conditions for either almost sure convergence or convergence in distribution of some well-known L-statistics and U-statistics. A law of the logarithm for weighted sums of order statistics is stated with no proof.
Descriptors : *ORDER STATISTICS, *STATISTICAL PROCESSES, RANDOM VARIABLES, STATISTICAL SAMPLES, CONVERGENCE, STATISTICAL DISTRIBUTIONS, LOGARITHM FUNCTIONS, ITERATIONS, DISTRIBUTION FUNCTIONS.
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE