Asymptotic Normality of Random Sums of m-dependent Random Variables

2013/03/10 by Ümi̇t Işlak, Umit Islak, Islak, Umit
Computer Science · Decision Sciences · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1303.2386

10 pages

arxiv created 2013/03/10 · openalex publication_date 2013/03/10 · arxiv updated 2013/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a central limit theorem for random sums of the form ∑_i=1^N_n X_i, where \X_i\_{i ≥ 1} is a stationary m-dependent process and N_n is a random index independent of \X_i\_{i≥ 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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