Convolution Metrics and Rates of Convergence in the CLT (Central Limit Theorem).

Abstract

Let (B,) be a complete separable Banach space and let X=X (B) be the vector space of all random variables defined on a probability space (Omega, A, P) and taking values in B. It is known that metrics on X of convolution type enjoy a variety of interesting properties. In this article it is shown that convolution metrics may also by used to obtain rates of convergence in CLT's involving a stable limit law. The rates are expressed in terms of a variety of uniform metrics on X and include the total variation metric and the uniform metrics between density and characteristic functions. The results represent both an improvement and an extension of existing results. Week convergence properties of convolution metrics are also explored. Keywords: Ideal probability metrics; Convolution metrics; Rate of convergence; Stable random variables.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1987
Accession Number
ADA189341

Entities

People

  • J. E. Yukich
  • S. T. Rachev

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Banach Space
  • Classification
  • Convergence
  • Distribution Functions
  • Gaussian Processes
  • Inequalities
  • Mathematics
  • North Carolina
  • Notation
  • Probability
  • Random Variables
  • Security
  • Sequences
  • Statistics
  • Stochastic Processes
  • Universities
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Organizational Process Management (OPM).
  • Statistical inference.

Technology Areas

  • Space