Complete moment convergence for randomly weighted sums of extended negatively dependent random variables with application to semiparametric regression models

Abstract

In this paper, we investigate the complete moment convergence for randomly weighted sums of extended negatively dependent (END) random variables. The results obtained in this paper extended the corresponding one of Li et al. (J Inequalities Appl 2017:16, 2017). As an application, we study the complete consistency for the estimator of semiparametric regression models based on END random variables by using the complete convergence that we established. Finally, we have conducted comprehensive simulation studies to demonstrate the validity of obtained theoretical results.

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Acknowledgements

The authors are most grateful to the Editor and anonymous referee for carefully reading the manuscript and valuable suggestions which helped in improving an earlier version of this paper. Supported by the National Natural Science Foundation of China (11871072, 12001105), the Natural Science Foundation of Anhui Province (1908085QA01, 1908085QA07), the Provincial Natural Science Research Project of Anhui Colleges (KJ2019A0003), and the Postdoctoral Science Foundation of China (2019M660156).

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Correspondence to Xuejun Wang.

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Cheng, N., Lu, C., Qi, J. et al. Complete moment convergence for randomly weighted sums of extended negatively dependent random variables with application to semiparametric regression models. Stat Papers (2021). https://doi.org/10.1007/s00362-021-01244-1

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Keywords

  • Extended negatively dependent random variables
  • Complete moment convergence
  • Randomly weighted sums
  • Semiparametric regression models
  • Complete consistency

Mathematics Subject Classification

  • 60F15
  • 62G05
  • 62G20