Moment Inequalities for Sn Under General Dependence Restrictions, with Applications.

Abstract

Consider a sum composed of a sequence of random variables and a sequence of constants. This paper establishes moment inequalities with dependence restrictions imposed upon the random variables but not depending upon the constants. A further inequality of more complicated form is also established. The dependence restrictions considered are either of the weak multiplicative type or of related types, namely exchangeable sequences and strongly mixing sequences. Three applications are developed. One treats the almost sure convergence of series under mild dependence restrictions and finite limit conditions. Secondly, an improved technique is presented for the problem of establishing the rate of convergence in the central limit theorem for simple linear rank statistics. Finally, the central limit theorem for strongly mixing summands is treated.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
May 01, 1977
Accession Number
ADA042682

Entities

People

  • M. Longnecker
  • Robert Serfling

Organizations

  • Florida State University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Convergence
  • Data Science
  • Distribution Functions
  • Distribution Theory
  • Gaussian Processes
  • Inequalities
  • Information Science
  • Mathematics
  • Normal Distribution
  • Probability
  • Random Variables
  • Sequences
  • Stationary Processes
  • Statistical Analysis
  • Statistics
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.