Complete convergence for weighted sums of AANA random variables and its application in nonparametric regression models
J. Korean Math. Soc.
Published online December 15, 2020
Aiting Shen and Yajing Zhang
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 Roenthel 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
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