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On the order of approximation in the random central limit theorem for m-dependent random variables

Rao B. L. S. P., Sreehari M.

Probability and Mathematical Statistics

2016

Vol. 36, Fasc. 1

47--57

We consider a random number Nn of m-dependent random variables Xk with a common distribution and the partial sums SNn = ΣNnj=1 Xj, where the random variable Nn is independent of the sequence of random variables {Xk, k ≥ 1} for every n ≥ 1. Under certain conditions on the random variables Xk and Nn, we obtain the limit distribution of the sequence SNn and the corresponding rate of convergence after suitable normalization.