Complete f-moment convergence for weighted sums of asymptotically almost negatively associated random variables and its application in semiparametric regression models

Abstract

In this paper, we investigate the complete f-moment convergence for weighted sums of asymptotically almost negatively associated (AANA, for short) random variables. Our results improve and generalize the corresponding ones of [M.M. Xi, X. Deng, X.J. Wang, and Z.Y. Cheng, $L^p$ convergence and complete convergence for weighted sums of AANA random variables, Commun. Stat. Theory Methods 47(22) (2018), pp. 5604–5613]. As an application of our main results, some results on the complete consistency for the estimator in semiparametric regression models are obtained and a simulation study is provided to assess the finite sample performance of the theoretical results.

Keywords:

• Complete f-moment convergence
• asymptotically almost negatively associated random variables
• semiparametric regression models

Mathematical Subject Classifications:

• 60F15
• 62G20

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Supported by the National Social Science Foundation of China (22BTJ059).