Asymptotic Normality of Random Sums of m-dependent Random Variables

Umit Islak

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arXiv · 1303.2386

Asymptotic Normality of Random Sums of m-dependent Random Variables

Umit Islak

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Abstract

We prove a central limit theorem for random sums of the form $\sum_{i=1}^{N_n} X_i$, where $\{X_i\}_{i \geq 1}$ is a stationary $m-$dependent process and $N_n$ is a random index independent of $\{X_i\}_{i\geq 1}$. Our proof is a generalization of Chen and Shao's result for i.i.d. case and consequently we recover their result. Also a variation of a recent result of Shang on $m-$dependent sequences is obtained as a corollary. Examples on moving averages and descent processes are provided, and possible applications on non-parametric statistics are discussed.

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Umit Islak. 2013-03-10. Asymptotic Normality of Random Sums of m-dependent Random Variables. https://arxiv.org/abs/1303.2386

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