Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1150919 | Statistical Methodology | 2012 | 9 Pages |
Abstract
Let {Xni,un⩽i⩽vn,n⩾1}{Xni,un⩽i⩽vn,n⩾1} and {Ani,un⩽i⩽vn,n⩾1}{Ani,un⩽i⩽vn,n⩾1} be two arrays of random variables. A new concept of integrability for an array of random variables {Xni}{Xni} with respect to an array of random variables {Ani}{Ani} is introduced. Under these notions of integrability and appropriate conditions on the array of random weights, strong laws of large numbers and mean convergence theorems for the randomly weighted sums ∑i=unvn(AniXni−EAniXni) are obtained. Our results extend and sharpen the known results in the literature.
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Xueping Hu, Guohua Fang,