Strong convergence properties for weighted sums of m-asymptotic negatively associated random variables and statistical applications

Yi Wu, Xuejun Wang and Aiting Shen ()
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Yi Wu: Anhui University
Xuejun Wang: Anhui University
Aiting Shen: Anhui University

Statistical Papers, 2021, vol. 62, issue 5, No 6, 2169-2194

Abstract: Abstract In this paper, we establish a general result on complete moment convergence and the Marcinkiewicz–Zygmund-type strong law of large numbers for weighted sums of m-asymptotic negatively associated random variables, which improve and extend some existing ones. As applications of our main results, we present a result on complete consistency for the weighted estimator in a nonparametric regression model and a result on strong consistency for conditional Value-at-risk estimator based on m-asymptotic negatively associated errors. We also carry out some numerical simulations to confirm the theoretical results.

Keywords: m-Asymptotic negatively associated random variables; Complete moment convergence; Complete convergence; Strong law of large numbers; Nonparametric regression model; Conditional value-at-risk; Complete consistency; Strong consistency; 60F15; 62G05 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00362-020-01179-z

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