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Complete convergence for weighted sums of random variables satisfying generalized Rosenthal-type inequalities*

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Abstract

In the paper, we establish the complete convergence for weighted sums of random variables satisfying generalized Rosenthal-type inequalities. Our results partially extend some known results and weaken their conditions. As statistical applications, we study the nonparametric regression model and obtain the complete consistency of the weighted regression estimator for the unknown regression functions.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Henan Normal University, Henan Province, 453007, China

    Chang Liu & Yu Miao

  2. Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, Henan Normal University, Henan Province, 453007, China

    Yu Miao

Authors
  1. Chang Liu
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  2. Yu Miao
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Correspondence to Yu Miao.

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This work is supported by National Natural Science Foundation of China (NSFC-11971154).

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Liu, C., Miao, Y. Complete convergence for weighted sums of random variables satisfying generalized Rosenthal-type inequalities*. Lith Math J 64, 18–33 (2024). https://doi.org/10.1007/s10986-024-09618-2

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  • DOI: https://doi.org/10.1007/s10986-024-09618-2

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