The Annals of Statistics

Khinchine’s theorem and Edgeworth approximations for weighted sums

Sergey G. Bobkov

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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.

Article information

Source
Ann. Statist., Volume 47, Number 3 (2019), 1616-1633.

Dates
Received: October 2017
Revised: May 2018
First available in Project Euclid: 13 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.aos/1550026851

Digital Object Identifier
doi:10.1214/18-AOS1728

Mathematical Reviews number (MathSciNet)
MR3911124

Zentralblatt MATH identifier
07053520

Subjects
Primary: 60F05: Central limit and other weak theorems

Keywords
Central limit theorem Edgeworth approximations

Citation

Bobkov, Sergey G. Khinchine’s theorem and Edgeworth approximations for weighted sums. Ann. Statist. 47 (2019), no. 3, 1616--1633. doi:10.1214/18-AOS1728. https://projecteuclid.org/euclid.aos/1550026851


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References

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