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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1616-1633 |
| Number of pages | 18 |
| Journal | Annals of Statistics |
| Volume | 47 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jan 2019 |
Bibliographical note
Funding Information:Received October 2017; revised May 2018. 1Supported in part by the NSF Grant DMS-1612961 and the Russian Academic Excellence Project “5-100.” MSC2010 subject classifications. 60F05. Key words and phrases. Central limit theorem, Edgeworth approximations.
Funding Information:
1Supported in part by the NSF Grant DMS-1612961 and the Russian Academic Excellence Project “5-100.” We would like to thank the referee for a careful reading of the manuscript and useful remarks.
Publisher Copyright:
© Institute of Mathematical Statistics, 2019.
Keywords
- Central limit theorem
- Edgeworth approximations