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Complete f-moment convergence for arrays of random variables and its applications in semiparametric and EV regression models

He Yongping, Shen Yan, Wang Rui, Wang Xuejun

Probability and Mathematical Statistics

2024

Vol. 44, Fasc. 1

87--118

We study the complete f-moment convergence for arrays of rowwise random variables satisfying a Rosenthal type moment inequality, and then establish general results on the complete moment convergence and complete convergence for partial sums and weighted sums of arrays of rowwise random variables. As applications, we further describe the statistical properties of complete f-moment convergence in both semiparametric regression models and simple linear errors-in-variables models. The asymptotic properties for estimators are established. We also provide some simulations to verify the validity of the theoretical results.

Complete f-moment convergence of moving average process and its application to nonparametric regression models

Yao Chi, Wang Rui, Chen Ling, Wang Xueyun

Probability and Mathematical Statistics

2021

Vol. 41, Fasc. 2

373--395

In this paper, we establish a general result on complete f-moment convergence of the moving average process based on widely orthant dependent random variables, which generalizes some results in the literature. In addition, an application of complete consistency to nonparametric regression models is provided. Finally, we provide a numerical simulation to verify the validity of our theoretical results.