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June 2019 Khinchine’s theorem and Edgeworth approximations for weighted sums
Sergey G. Bobkov
Ann. Statist. 47(3): 1616-1633 (June 2019). DOI: 10.1214/18-AOS1728

Abstract

Let $F_{n}$ denote the distribution function of the normalized sum of $n$ i.i.d. random variables. In this paper, polynomial rates of approximation of $F_{n}$ by the corrected normal laws are considered in the model where the underlying distribution has a convolution structure. As a basic tool, the convergence part of Khinchine’s theorem in metric theory of Diophantine approximations is extended to the class of product characteristic functions.

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Sergey G. Bobkov. "Khinchine’s theorem and Edgeworth approximations for weighted sums." Ann. Statist. 47 (3) 1616 - 1633, June 2019. https://doi.org/10.1214/18-AOS1728

Information

Received: 1 October 2017; Revised: 1 May 2018; Published: June 2019
First available in Project Euclid: 13 February 2019

zbMATH: 07053520
MathSciNet: MR3911124
Digital Object Identifier: 10.1214/18-AOS1728

Subjects:
Primary: 60F05

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 3 • June 2019
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