Multivariate Normal Approximation by Stein's Method: The Concentration Inequality Approach

2011/11/17 by Chen, Louis H. Y., Fang, Xiao
#60B10 #60F05 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1111.4073

Abstract

The concentration inequality approach for normal approximation by Stein's method is generalized to the multivariate setting. We use this approach to prove a non-smooth function distance for multivariate normal approximation for standardized sums of k-dimensional independent random vectors W=∑_i=1ⁿ X_i with an error bound of order k^1/2γ where γ=∑_i=1ⁿ E|X_i|³. For sums of locally dependent (unbounded) random vectors, we obtain a fourth moment bound which is typically of order O_k(1/√(n)), as well as a third moment bound which is typically of order O_k(log n/√(n)).

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