Asymptotic results for random sums of dependent random variables

Ümit Işlak

Statistics & Probability Letters, 2016, vol. 109, issue C, 22-29

Abstract: Our main result is a central limit theorem for random sums of the form ∑i=1NnXi, where {Xi}i≥1 is a stationary m-dependent process and Nn is a random index independent of {Xi}i≥1. This extends the work of Chen and Shao on the i.i.d. case to a dependent setting and provides a variation of a recent result of Shang on m-dependent sequences. Further, a weak law of large numbers is proven for ∑i=1NnXi, and the results are exemplified with applications on moving average and descent processes.

Keywords: Stein’s method; Random sums; Central limit theorem; Concentration inequality; Local dependence (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.spl.2015.10.015

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