The Law of the Iterated Logarithm and Central Limit Theorem for L-Statistics.

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.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1997
Accession Number
ADA328387

Entities

People

  • Deli Li
  • M. B. Rao
  • R. J. Tomkins

Organizations

  • Pennsylvania State University

Tags

DTIC Thesaurus Topics

  • Asymptotic Normality
  • Data Science
  • Distribution Functions
  • Information Science
  • Mathematics
  • Multivariate Analysis
  • New York
  • Normal Distribution
  • Numbers
  • Order Statistics
  • Probability
  • Random Variables
  • Real Numbers
  • Sequences
  • Statistics
  • United States
  • United States Government

Fields of Study

  • Mathematics

Readers

  • Statistical inference.
  • Theoretical Analysis.