On short Edgeworth expansions for weighted sums of random vectors

2023/12/22 by Sagak A. Ayvazyan, Ayvazyan, Sagak
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2312.14696

openalex publication_date 2023/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The "typical" asymptotic behavior of the weighted sums of independent, identically distibuted random vectors in k-dimensional space is considered. It is shown that under finitnes of fifth absolute moment of an individual term the rate of convergence by Edgeworth correction in the multivariate central limit theorem is of order O(1/n³/2 ). This extends the one-dimensional Bobkov(2020) result.

Related

• Estimates for the strong approximation in multidimensional central limit theorem
• Edgeworth expansions for independent bounded integer valued random variables
• Asymptotic Expansions in Free Limit Theorems
• Asymptotic distribution of independent random vectors given their sum
• A Uniform-in-P Edgeworth Expansion under Weak Cramér Conditions