Normal Approximation for Weighted Sums under a Second Order Correlation Condition

2019/06/21 by Sergey G. Bobkov, Bobkov, S. G., G. P. Chistyakov +3 · 1 citation
Mathematics · #60E #60F #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Point processes and geometric inequalities #Probability (math.PR) #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1906.09063

openalex publication_date 2019/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Under correlation-type conditions, we derive an upper bound of order (log n)/n for the average Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law. The result is based on improved concentration inequalities on high-dimensional Euclidean spheres. Applications are illustrated on the example of log-concave probability measures.

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• The KLS constant is O(log^1/4 n)

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