Complete convergence for weighted sums of AANA random variables and its application in nonparametric regression models
J. Korean Math. Soc. 2021 Vol. 58, No. 2, 327-349
https://doi.org/10.4134/JKMS.j200029
Published online December 15, 2020
Printed March 1, 2021
Aiting Shen, Yajing Zhang
Anhui University; Anhui University
Abstract : In this paper, we main study the strong law of large numbers and complete convergence for weighted sums of asymptotically almost negatively associated (AANA, in short) random variables, by using the Marcinkiewicz-Zygmund type moment inequality and Roenthal type moment inequality for AANA random variables. As an application, the complete consistency for the weighted linear estimator of nonparametric regression models based on AANA errors is obtained. Finally, some numerical simulations are carried out to verify the validity of our theoretical result.
Keywords : Asymptotically almost negatively associated random variables, strong law of large numbers, complete convergence, nonparametric regression model, complete consistency
MSC numbers : 60F15, 62G20
Supported by : Supported by the National Natural Science Foundation of China (11871072, 11701005), the Natural Science Foundation of Anhui Province (1608085QA02, 1808085QA17), and the Provincial Natural Science Research Project of Anhui Colleges (KJ2019A0003)
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