Asymptotic results for random sums of dependent random variables
| Autor: | Ümit Işlak |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Statistics and Probability
010102 general mathematics Stein's method 01 natural sciences Combinatorics 010104 statistics & probability Convergence of random variables Moving average Law of large numbers Dependent random variables 0101 mathematics Statistics Probability and Uncertainty Concentration inequality Mathematics Descent (mathematics) Central limit theorem |
| Zdroj: | Statistics & Probability Letters. 109:22-29 |
| ISSN: | 0167-7152 |
| DOI: | 10.1016/j.spl.2015.10.015 |
| Popis: | Our main result is 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 . 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 = 1 N n X i , and the results are exemplified with applications on moving average and descent processes. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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