Equivalent conditions of convergence properties for m-ANA sequence and statistical applications

Miaomiao Wang, Min Wang, Xuejun Wang and Fei Zhang

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 5, 1547-1575

Abstract: In this paper, the seven equivalent conditions of complete moment convergence and complete integral convergence for m-asymptotic negatively associated (m-ANA, for short) random variables are established. The results obtained in the paper extend and improve some corresponding ones for negatively associated (NA, for short) random variables and negatively orthant dependent (NOD, for short) random variables. As an application of our main results, we present a result on complete consistency for the weighted estimator in a nonparametric regression model based on m-ANA errors. We perform a numerical simulation to verify the validity of the theoretical results.

Date: 2024
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DOI: 10.1080/03610926.2022.2106575

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