Non-uniform bounds for geometric approximation

M. J. Phillips and Graham V. Weinberg

Statistics & Probability Letters, 2000, vol. 49, issue 3, 305-311

Abstract: Crucial to the Stein-Chen method for distributional approximation is the estimation of differences of the solution to a Stein equation associated with the distributions being compared, and the usual approach has been to obtain uniform bounds on these differences. The purpose of this paper is to demonstrate, in the geometric case, that improvement can be obtained by taking non-uniform bounds. The results are illustrated with an application to Pólya distribution convergence.

Keywords: Geometric; approximation; Non-uniform; bounds; Immigration-birth-death; process; Stein-Chen; method; Total; variation; distance; Polya; distribution (search for similar items in EconPapers)
Date: 2000
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