Acta Mathematica Sinica, English Series

, Volume 35, Issue 12, pp 1917–1936

# Complete f-moment Convergence for Widely Orthant Dependent Random Variables and Its Application in Nonparametric Models

• Chao Lu
• Zhuang Chen
• Xue Jun Wang
Article

## Abstract

In this paper, we study the complete f-moment convergence for widely orthant dependent (WOD, for short) random variables. A general result on complete f-moment convergence for arrays of rowwise WOD random variables is obtained. As applications, we present some new results on complete f-moment convergence for WOD random variables. We also give an application to nonparametric regression models based onWOD errors by using the complete convergence that we established. Finally, the choice of the fixed design points and the weight functions for the nearest neighbor estimator are proposed, and a numerical simulation is provided to verify the validity of the theoretical result.

## Key words

Widely orthant dependent random variables complete f-moment convergence complete convergence complete consistency

60F15 60G20

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