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The consistency for the estimator of nonparametric regression model based on martingale difference errors

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Abstract

In this paper, by using the inequalities for martingale difference sequence, we investigate the consistency for the estimator of nonparametric regression model based on martingale difference errors. Some results on consistency for the estimator of \(g(x)\) are presented, including the mean consistency, complete consistency and strong consistency. As an application, the consistency for the nearest neighbor estimator is obtained.

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Acknowledgments

The authors are most grateful to the Editor Christine H. Müller and anonymous referees for careful reading of the manuscript and valuable suggestions which helped significantly improving an earlier version of this paper. Supported by the National Natural Science Foundation of China (11471272,11201001, 11171001), the Science Fund for Distinguished Young Scholars of Anhui Province (1508085J06), the Natural Science Foundation of Fujian Province (2013J01019) and Anhui Province (1308085QA03, 1408085QA02).

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    Zhiyong Chen & Haibin Wang

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

    Xuejun Wang

  3. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637371, Singapore

    Xuejun Wang

Authors
  1. Zhiyong Chen
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  2. Haibin Wang
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  3. Xuejun Wang
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Correspondence to Xuejun Wang.

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Chen, Z., Wang, H. & Wang, X. The consistency for the estimator of nonparametric regression model based on martingale difference errors. Stat Papers 57, 451–469 (2016). https://doi.org/10.1007/s00362-015-0662-6

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  • DOI: https://doi.org/10.1007/s00362-015-0662-6

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