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Complete q-th moment convergence and its statistical applications

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this paper, we mainly investigate the complete q-th moment convergence for sums of widely orthant dependent random variables by utilizing the Rosenthal type moment inequality and truncation method. Some sufficient conditions for the complete q-th moment convergence are provided. The results obtained in the paper generalize some corresponding ones of negatively associated random variables in the literature. As an application, the complete consistency for the weighted estimator in a nonparametric regression model is established, and the simulation studies are presented to show the consistency for the nearest neighbor weight function estimator in a nonparametric regression model.

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Acknowledgements

The authors are most grateful to the Editor and anonymous referees for carefully reading the manuscript and valuable suggestions, which helped in improving an earlier version of this paper.

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  1. School of Mathematical Sciences, Anhui University, Hefei, 230601, People’s Republic of China

    Aiting Shen & Caoqing Wu

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  1. Aiting Shen
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  2. Caoqing Wu
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Supported by the National Natural Science Foundation of China (11871072, 11701005) and the Provincial Natural Science Research Project of Anhui Colleges (KJ2019A0003).

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Shen, A., Wu, C. Complete q-th moment convergence and its statistical applications. RACSAM 114, 35 (2020). https://doi.org/10.1007/s13398-019-00778-2

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