Asymptotic Expansions and Two-Sided Bounds in Randomized Central Limit Theorems

Sergey G. Bobkov; Gennadiy P. Chistyakov; Friedrich Götze

doi:10.1007/978-3-031-26300-2_3

Asymptotic Expansions and Two-Sided Bounds in Randomized Central Limit Theorems

Sergey G. Bobkov, Gennadiy P. Chistyakov, Friedrich Götze

Mathematics

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Abstract

Lower and upper bounds are explored for the uniform (Kolmogorov) and L² -distances between the distributions of weighted sums of dependent summands and the normal law. The results are illustrated for several classes of random variables whose joint distributions are supported on Euclidean spheres. We also survey several results on improved rates of normal approximation in randomized central limit theorems.

Original language	English (US)
Title of host publication	Lecture Notes in Mathematics
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	67-128
Number of pages	62
DOIs	https://doi.org/10.1007/978-3-031-26300-2_3
State	Published - 2023

Publication series

Name	Lecture Notes in Mathematics
Volume	2327
ISSN (Print)	0075-8434
ISSN (Electronic)	1617-9692

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Keywords

Central limit theorem
Normal approximation
Typical distributions

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10.1007/978-3-031-26300-2_3

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KW - Typical distributions

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Asymptotic Expansions and Two-Sided Bounds in Randomized Central Limit Theorems

Abstract

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