Khinchine’s theorem and Edgeworth approximations for weighted sums
The Annals of Statistics · 2019 · Volume 47 · Issue 3
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.
Keywords
60F05, central limit theorem, Edgeworth approximations
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