On complete and complete moment convergence for weighted sums of ANA random variables and applications. Issue 15 (13th October 2019)

• Record Type: Journal Article
• Authors: Chen, Zhuang; Lu, Chao; Shen, Yan; Wang, Rui; Wang, Xuejun
• Is Part Of: Journal of statistical computation and simulation. Volume 89:Issue 15(2019)
• Page Start: 2871
• Page End: 2898
• Publication Date: 2019-10-13
• Subjects: ANA random variables -- complete moment convergence -- complete convergence -- nonparametric regression model -- complete consistency; 60F15 -- 62G20; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2019.1643346
• Languages: English
• ISSNs: 0094-9655

Abstract

ABSTRACT: In this article, the complete convergence and complete moment convergence for weighted sums of asymptotically negatively associated (ANA, for short) random variables are studied. Several sufficient conditions of the complete convergence and complete moment convergence for weighted sums of ANA random variables are presented. As an application, the complete consistency for the weighted estimator in a nonparametric regression model based on ANA random errors is established by using the complete convergence that we established. We also give a simulation to verify the validity of the theoretical result.