A general result on complete convergence for weighted sums of linear processes and its statistical applications. Issue 4 (4th July 2019)

• Record Type: Journal Article
• Authors: Deng, Xin; Wang, Xuejun; Hu, Shuhe; Hu, Ming
• Is Part Of: Statistics. Volume 53:Issue 4(2019)
• Page Start: 903
• Page End: 920
• Publication Date: 2019-07-04
• Subjects: Linear process -- complete convergence -- semiparametric regression model -- nonparametric regression model -- complete consistency; 62F12 -- 62G05 -- 60F15; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2019.1615912
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: Consider the linear process X i = ∑ j = − ∞ ∞ ψ j e i − j, where { e i } is a sequence of identically distributed, negatively associated random variables with E e 0 = 0, and { ψ j } is a sequence of real numbers with ∑ j = − ∞ ∞ | ψ j | < ∞ . Under some mild conditions, we first establish a general result on complete convergence for weighted sums of such linear process, and then describe its statistical properties and interpretations in both semiparametric and nonparametric regression models. We also prove the complete consistency for the parameter estimators. In addition, we have conducted comprehensive simulation studies to demonstrate the validity of obtained theoretical results.