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The Consistency for the Estimators of Semiparametric Regression Model with Dependent Samples

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Abstract

For the semiparametric regression model: \(Y^{(j)}(x_{in},t_{in})=t_{in}\beta+g(x_{in})+e^{(j)}(x_{in})\), 1 ≤ j ≤ k, 1≤ i ≤ n, where tin ∈ ℝ and xin ∈ ℝp are known to be nonrandom, g is an unknown continuous function on a compact set A in ℝp, ej(xin) are m-extended negatively dependent random errors with mean zero, Y(j)(xin, tin) represent the j-th response variables which are observable at points xin, tin. In this paper, we study the strong consistency, complete consistency and r-th (r > 1) mean consistency for the estimators βk,n and gk,n of β and g, respectively. The results obtained in this paper markedly improve and extend the corresponding ones for independent random variables, negatively associated random variables and other mixing random variables. Moreover, we carry out a numerical simulation for our main results.

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Acknowledgments

The authors are very grateful to the anonymous referees and the editor for their valuable comments and suggestions.

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Authors and Affiliations

  1. School of Big Data and Artificial Intelligence, Chizhou University, Chizhou, 247000, China

    Yi Wu

  2. School of Mathematical Sciences, Anhui University, Hefei, 230601, China

    Yi Wu, Xue-jun Wang, Ling Chen & Kun Jiang

Authors
  1. Yi Wu
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  2. Xue-jun Wang
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  3. Ling Chen
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  4. Kun Jiang
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Corresponding author

Correspondence to Xue-jun Wang.

Additional information

This paper is supported by the National Natural Science Foundation of China (11671012, 11871072), the Natural Science Foundation of Anhui Province (1808085QA03, 1908085QA01, 1908085QA07), and the Provincial Natural Science Research Project of Anhui Colleges (KJ2019A0003).

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Wu, Y., Wang, Xj., Chen, L. et al. The Consistency for the Estimators of Semiparametric Regression Model with Dependent Samples. Acta Math. Appl. Sin. Engl. Ser. 37, 299–318 (2021). https://doi.org/10.1007/s10255-021-1008-x

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  • DOI: https://doi.org/10.1007/s10255-021-1008-x

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