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On the Bahadur Representation of Quantiles for a Sample from ρ*-Mixing Structure Population

Dudek Dagmara, Kuczmaszewska Anna

Advances in Science and Technology. Research Journal

2022

Vol. 16, no 3

316--330

In this paper, we establish the strong consistency and the Bahadur representation of sample quantiles for ρ*-mixing random variables. Additionally, the asymptotic normality and the Berry-Esseen bound of sample quantiles for ρ*-mixing random variables are presented. Additionally, we provide the rate of convergence of sample quantiles to population counterparts. Moreover, numerical simulation is presented to ilustrate and verify obtained results.

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.