Complete moment convergence for double-indexed randomly weighted sums and its applications. Issue 3 (4th May 2018) - Wang, Xuejun; Wu, Yi; Hu, Shuhe
ABSTRACT: In this paper, we mainly study the complete moment convergence of double-indexed randomly weighted sums of negatively superadditive-dependent (NSD, for short) random variables, which is stronger than complete convergence. In addition, theL r convergence of double-indexed randomly weighted sums of NSD random variables is also obtained. As applications, we obtain the complete consistency for the randomly weighted estimator in a nonparametric regression model based on NSD errors, and study the almost sure convergence and mean square convergence of the state observers of linear-time-invariant systems.