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