Complete convergence for weighted sums of arrays of random elements
Abstract
Let{Xnk:k,n=1,2,…}be an array of row-wise independent random elements in a separable Banach space. Let{ank:k,n=1,2,…}be an array of real numbers such that∑k=1∞|ank|≤1and∑n=1∞exp(−α/An)∞for eachα ϵ R+whereAn=∑k=1∞ank2. The complete convergence of∑k=1∞ankXnkis obtained under varying moment and distribution conditions on the random elements. In particular, laws of large numbers follow for triangular arrays of random elements, and consistency of the kernel density estimates is obtained from these results.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jan 01, 1983
- Source ID
- 10.1155/s0161171283000046
Entities
People
- Robert Lee Taylor
Organizations
- Air Force Office of Scientific Research
- University of South Carolina