Sufficient and necessary conditions of convergence properties for ANA sequences with an application to EV regression models

Jinxiang Ou, Miaomiao Wang, Yao Wang, Tao Lv, Qiong Wu and Xuejun Wang

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 15, 4710-4736

Abstract: In this article, we investigate the complete moment convergence and the Marcinkiewicz-Zygmund-type strong law of large numbers (SLLN, for short) for weighted sums of asymptotically negatively associated (ANA, for short) random variables. The results generalize and improve the corresponding one of Vu et al. (J. Theor. Probab. 34: 331-348, 2021) to the case of ANA random variables. With some properties of slowly varying function, three equivalent conditions of convergence properties for ANA sequences are established, as well as the SLLN for weighted sums of ANA random variables. As an application, the strong consistency of the least squared (LS, for short) estimators in an errors-in-variables (EV, for short) model based on ANA random errors is established. We also give a simulation to support the theoretical result based on finite samples.

Date: 2025
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DOI: 10.1080/03610926.2024.2427228

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