On the rate of convergence in the central limit theorem for arrays of random vectors

TitleOn the rate of convergence in the central limit theorem for arrays of random vectors
Publication TypeJournal Article
Year of Publication2020
AuthorsVan Dung, L, Son, TCong
JournalStatistics & Probability Letters
Volume158
Pagination108671
ISSN0167-7152
KeywordsCentral limit theorem, Convergence rate, Multivariate normal, Normal approximation, Random vector
Abstract

Let Xn,i;1≤i≤kn,n≥1 be an array of martingale difference random vectors and kn;n≥1 a sequence of positive integers such that kn→∞ as n→∞. The aim of this paper is to establish the rate of convergence for the central limit theorem for the sum Sn=Xn,1+Xn,1+...+Xn,kn. We also show that for stationary sequences of martingale difference random vectors, under condition E(‖X1‖2+2δ)<∞ for some δ≥1∕2, the rate n−δ∕(2+2δ)logn is reached, this rate is better than n−1∕4 for δ>1.

URLhttp://www.sciencedirect.com/science/article/pii/S0167715219303177
DOI10.1016/j.spl.2019.108671