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COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF AANA RANDOM VARIABLES AND ITS APPLICATION IN NONPARAMETRIC REGRESSION MODELS

  • Shen, Aiting (School of Mathematical Sciences Anhui University) ;
  • Zhang, Yajing (School of Mathematical Sciences Anhui University)
  • Received : 2020.01.16
  • Accepted : 2020.07.21
  • Published : 2021.03.01

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.