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Article

KHINCHINE’S THEOREM AND EDGEWORTH APPROXIMATIONS FOR WEIGHTED SUMS

Annals of Statistics. 2019. Vol. 47. No. 3. P. 1616-1633.

Let F_n denote the distribution function of the normalized sum of ni.i.d. random variables. In this paper, polynomial rates of approx- imation of Fn 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 met- ric theory of Diophantine approximations is extended to the class of product characteristic functions.