Strong Convergence Theorems Under Sub-linear Expectations and Its Applications in Nonparametric Regression Models

Abstract

In this paper, we first study the complete convergence for arrays of rowwise widely orthant dependent random variables under sub-linear expectations. The complete convergence theorems are established in sense of sub-additive capacities under some mild conditions. As an application of the main results, we investigate the strong consistency for the weighted estimator in a nonparametric regression model based on widely orthant dependent errors under sub-linear expectations. In addition, we also obtain the rate of strong consistency for the estimator in a nonparametric regression model based on widely orthant dependent errors under sub-linear expectations.

Keywords

Complete convergence / Capacity / Sub-linear expectations / Widely orthant dependent random variables / Strong consistency / 60F15 / 62G05

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Funding

national natural science foundation of china(11871072)

Natural Science Foundation of Anhui Province(2108085MA06, 2108085QA15, 1908085QA01, 1908085QA07)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature