Asymptotic Expansions and two-sided Bounds in Randomized Central Limit Theorems

2023/08/04 by Sergey G. Bobkov, Bobkov, S. G., G. P. Chistyakov +3
Decision Sciences · Mathematics · #60E #60F #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Probability and Risk Models #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2308.02693

openalex publication_date 2023/08/04 · openalex created_date 2023/08/09 · openalex updated_date 2026/07/28

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.

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