Random central limit theorem for associated random variables and the order of approximation

摘要

We consider a random number N-n and strictly stationary associated random variables X-k and form random partial sums S-Nn = Sigma(Nn)(j=1) X-j under the assumption that N-n is independent of the sequence {X-r,X- r >= 1} for every n >= 1. Under certain conditions on the random variables X-k and N-n, we obtain the limit distribution of the sequence S-Nn after suitable normalization. We also obtain an estimate of the order of approximation. (C) 2016 Elsevier B.V. All rights reserved.