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

Yi Wu , Xin Deng , Mengmei Xi , Xuejun Wang

Communications in Mathematics and Statistics ›› 2025, Vol. 13 ›› Issue (4) : 863 -889.

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Communications in Mathematics and Statistics ›› 2025, Vol. 13 ›› Issue (4) : 863 -889. DOI: 10.1007/s40304-023-00344-8
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Strong Convergence Theorems Under Sub-linear Expectations and Its Applications in Nonparametric Regression Models

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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.

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

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Yi Wu, Xin Deng, Mengmei Xi, Xuejun Wang. Strong Convergence Theorems Under Sub-linear Expectations and Its Applications in Nonparametric Regression Models. Communications in Mathematics and Statistics, 2025, 13(4): 863-889 DOI:10.1007/s40304-023-00344-8

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Funding

national natural science foundation of china(11871072)

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

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

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