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Optimal difference-based estimation for partially linear models

Author

Listed:
  • Yuejin Zhou

    (Anhui University of Science and Technology
    Zhejiang Gongshang University)

  • Yebin Cheng

    (Donghua University)

  • Wenlin Dai

    (King Abdullah University of Science and Technology)

  • Tiejun Tong

    (Hong Kong Baptist University)

Abstract

Difference-based methods have attracted increasing attention for analyzing partially linear models in the recent literature. In this paper, we first propose to solve the optimal sequence selection problem in difference-based estimation for the linear component. To achieve the goal, a family of new sequences and a cross-validation method for selecting the adaptive sequence are proposed. We demonstrate that the existing sequences are only extreme cases in the proposed family. Secondly, we propose a new estimator for the residual variance by fitting a linear regression method to some difference-based estimators. Our proposed estimator achieves the asymptotic optimal rate of mean squared error. Simulation studies also demonstrate that our proposed estimator performs better than the existing estimator, especially when the sample size is small and the nonparametric function is rough.

Suggested Citation

  • Yuejin Zhou & Yebin Cheng & Wenlin Dai & Tiejun Tong, 2018. "Optimal difference-based estimation for partially linear models," Computational Statistics, Springer, vol. 33(2), pages 863-885, June.
    • Handle: RePEc:spr:compst:v:33:y:2018:i:2:d:10.1007_s00180-017-0786-3
    DOI: 10.1007/s00180-017-0786-3
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    References listed on IDEAS

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