Complete convergence for weighted sums of END random variables and its application to nonparametric regression models

ABSTRACT

In this article, the complete convergence for weighted sums of extended negatively dependent (END, for short) random variables is investigated. Some sufficient conditions for the complete convergence are provided. In addition, the Marcinkiewicz–Zygmund type strong law of large numbers for weighted sums of END random variables is obtained. The results obtained in the article generalise and improve the corresponding one of Wang et al. [(2014b), ‘On Complete Convergence for an Extended Negatively Dependent Sequence’, Communications in Statistics-Theory and Methods, 43, 2923–2937]. As an application, the complete consistency for the estimator of nonparametric regression model is established.

KEYWORDS:

• Extended negatively dependent random variable
• complete convergence
• nonparametric regression model
• complete consistency

AMS SUBJECT CLASSIFICATION:

• 60F15
• 62G05

Acknowledgments

The author is most grateful to the Editor and two anonymous referees for careful reading of the manuscript and valuable suggestions which helped in improving an earlier version of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [11201001, 11501004, 11671012], the Natural Science Foundation of Anhui Province [1508085J06], the Key Projects for Academic Talent of Anhui Province [gxbjZD2016005], the Provincial Natural Science Research Project of Anhui Colleges [KJ2015A018], the Quality Engineering Project of Anhui Province [2015jyxm045], the Quality Improvement Projects for Undergraduate Education of Anhui University [ZLTS2015035] and the Doctoral Research Start-up Funds Projects of Anhui University.