Journal of the
Korean Mathematical Society JKMS

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)