Asymptotic results for random sums of dependent random variables

Umit Islak

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Our main result is a central limit theorem for random sums of the form ∑i=1Nn Xi, 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=1Nn, and the results are exemplified with applications on moving average and descent processes.

Original languageEnglish (US)
Pages (from-to)22-29
Number of pages8
JournalStatistics and Probability Letters
Volume109
DOIs
StatePublished - Feb 1 2016

Keywords

  • Central limit theorem
  • Concentration inequality
  • Local dependence
  • Random sums
  • Stein's method

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