Asymptotic results for random sums of dependent random variables
Statistics and Probability Letters, cilt.109, ss.22-29, 2016 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 109
- Basım Tarihi: 2016
- Doi Numarası: 10.1016/j.spl.2015.10.015
- Dergi Adı: Statistics and Probability Letters
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.22-29
- Anahtar Kelimeler: Central limit theorem, Concentration inequality, Local dependence, Random sums, Stein's method
- Boğaziçi Üniversitesi Adresli: Evet
Özet
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.