Complete moment convergence for double-indexed randomly weighted sums and its applications. Issue 3 (4th May 2018)

• Record Type: Journal Article
• Authors: Wang, Xuejun; Wu, Yi; Hu, Shuhe
• Is Part Of: Statistics. Volume 52:Issue 3(2018)
• Page Start: 503
• Page End: 518
• Publication Date: 2018-05-04
• Subjects: Complete moment convergence -- complete convergence -- randomly weighted sums -- nonparametric regression model -- state observers -- linear-time-invariant systems; 60F15 -- 62G05; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2018.1436548
• Languages: English
• ISSNs: 0233-1888

Abstract

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.