| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 10526758 | Statistics & Probability Letters | 2005 | 8 Pages |
Abstract
The convergence in probability of the sequence of sums âi=unvn(Xni-cni)/bn is obtained, where {un,n⩾1} and {vn,n⩾1} are sequences of integers, {Xni,un⩽i⩽vn,n⩾1} are random variables, {cni,un⩽i⩽vn,n⩾1} are constants or conditional expectations, and {bn,n⩾1} are constants satisfying bnââ as nââ. The work is proved under a Cesà ro-type condition which does not assume the existence of moments of Xni. The current work extends that of Gut (1992, Statist. Probab. Lett. 14, 49-52), Hong and Oh (1995, Statist. Probab. Lett. 22, 52-57), Hong and Lee (1996, Bull. Inst. Math. Acad. Sinica 24, 205-209), and Sung (1998, Statist. Probab. Lett. 38, 10-105).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Soo Hak Sung, Tien-Chung Hu, Andrei Volodin,