A Central Limit Theorem for $m$-Dependent Random Variables with Unbounded $m$

A More General Central Limit Theorem for M-dependent Random Variables with Unbounded M

In this article, a general central limit theorem for a triangular array of m-dependent random variables is presented. Here m may tend to innnity with the row index at a certain rate. Our theorem is a generalization of previous results. Some examples are given that show that the generalization is useful. In particular, we consider the limiting behavior of the sample mean of a running average pro...

Central and Local Limit Theories in Markov Dependent Random Variables

Wavelet Based Estimation of the Derivatives of a Density for m-Dependent Random Variables

Here, we propose a method of estimation of the derivatives of probability density based wavelets methods for a sequence of m−dependent random variables with a common one-dimensional probability density function and obtain an upper bound on Lp-losses for the such estimators.

Central Limit Theorems for Dependent Random Variables

1. Limiting distributions of sums of 'small' independent random variables have been extensively studied and there is a satisfactory general theory of the subject (see e.g. the monograph of B.V. Gnedenko and A.N. Kolmogorov [2]). These results are conveniently formulated for double arrays Xn k (k = 1, . . . , kn ; n = 1, 2, . . . ) of random variables where the Xn k (k = 1, . . . , kn), the rand...

central and local limit theories in markov dependent random variables