Abstract
We establish some results on the complete moment convergence for weighted sums of widely orthant-dependent (WOD) random variables, which improve and extend the corresponding results of Y. F. Wu, M. G. Zhai, and J. Y. Peng [J. Math. Inequal., 2019, 13(1): 251–260]. As an application of the main results, we investigate the complete consistency for the estimator in a nonparametric regression model based on WOD errors and provide some simulations to verify our theoretical results.
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Acknowledgements
The authors are most grateful to the anonymous referees for carefully reading the manuscript and valuable suggestions which helped in improving an earlier version of this paper. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11671012, 11871072), the Natural Science Foundation of Anhui Province (1808085QA03, 1908085QA01, 1908085QA07), the Provincial Natural Science Research Project of Anhui Colleges (KJ2019A0001, KJ2019A0003), and the Students Innovative Training Project of Anhui University (S201910357342).
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Cheng, L., Lang, J., Shen, Y. et al. Complete moment convergence for weighted sums of widely orthant-dependent random variables and its application in nonparametric regression models. Front. Math. China 17, 571–590 (2022). https://doi.org/10.1007/s11464-021-0915-8
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DOI: https://doi.org/10.1007/s11464-021-0915-8