Accession Number : ADA189341

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

Descriptive Note : Technical rept. Sep 87-Aug 88,

Corporate Author : NORTH CAROLINA UNIV AT CHAPEL HILL CENTER FOR STOCHASTIC PROCESSES

Personal Author(s) : Rachev, S T ; Yukich, J E

PDF Url : ADA189341

Report Date : Oct 1987

Pagination or Media Count : 39

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.

Descriptors :   *CONVERGENCE, *CONVOLUTION, BANACH SPACE, LIMITATIONS, PROBABILITY, RANDOM VARIABLES, RATES, SEPARATION, STABILITY, THEOREMS, VECTOR SPACES

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE