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

Le Van Dung and Ta Cong Son

Statistics & Probability Letters, 2020, vol. 158, issue C

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.

Keywords: Random vector; Multivariate normal; Normal approximation; Central limit theorem; Convergence rate (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spl.2019.108671

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