Complete convergence for weighted sums of negatively associated random variables
β Scribed by Han-Ying Liang
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 98 KB
- Volume
- 48
- Category
- Article
- ISSN
- 0167-7152
No coin nor oath required. For personal study only.
β¦ Synopsis
We discuss complete convergence for weighted sums of negatively associated (NA) random variables. The result on i.i.d. case of Li et al. (J. Theoret. Probab. 8 (1995) 49 -76) is generalized and extended. Also, Gut's (Probab. Theory Related Fields 97 (1993) 169 -178) result on CesΓ aro summation of i.i.d. random variables is extended.
π SIMILAR VOLUMES
Let [X n , n 1] be a sequence of stationary negatively associated random variables, Under some suitable conditions, the central limit theorem and the weak convergence for sums are investigated. Applications to limiting distributions of estimators of Var S n are also discussed.
Under general weighting coe cient, we obtain the complete convergence for weighted sums of negatively associated (NA) sequences, and discuss its necessity. The results on i.i.d. setting of Chow [
Let {X n ; n ΒΏ 0} be a sequence of negatively associated random variables. we consider its geometrically weighted series (ΓΏ) = β n = 0 ΓΏ n X n for 0 Β‘ ΓΏ Β‘ 1 and establish the LIL for (ΓΏ) as ΓΏ 1.
Strong laws of large numbers are established for the weighted sums of i.i.d. random variables which have higher-order moment condition. One of the results of Bai and Cheng (2000, Statist. Probab. Lett. 46, 105 -112) is extended.