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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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    1. Michael Lokshin, 2006. "Difference-based semiparametric estimation of partial linear regression models," Stata Journal, StataCorp LP, vol. 6(3), pages 377-383, September.
    2. Zhao, Haibing & You, Jinhong, 2011. "Difference based estimation for partially linear regression models with measurement errors," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1321-1338, November.
    3. Tiejun Tong & Yuedong Wang, 2005. "Estimating residual variance in nonparametric regression using least squares," Biometrika, Biometrika Trust, vol. 92(4), pages 821-830, December.
    4. Hongchang Hu & Yu Zhang & Xiong Pan, 2016. "Asymptotic normality of DHD estimators in a partially linear model," Statistical Papers, Springer, vol. 57(3), pages 567-587, September.
    5. Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-1092, November.
    6. Yatchew, A., 1997. "An elementary estimator of the partial linear model," Economics Letters, Elsevier, vol. 57(2), pages 135-143, December.
    7. Eubank, R. L. & Kambour, E. L. & Kim, J. T. & Klipple, K. & Reese, C. S. & Schimek, M., 1998. "Estimation in partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 29(1), pages 27-34, November.
    8. Germán Aneiros & Nengxiang Ling & Philippe Vieu, 2015. "Error variance estimation in semi-functional partially linear regression models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(3), pages 316-330, September.
    9. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    10. Levine, Michael, 2015. "Minimax rate of convergence for an estimator of the functional component in a semiparametric multivariate partially linear model," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 283-290.
    11. WenWu Wang & Lu Lin & Li Yu, 2017. "Optimal variance estimation based on lagged second-order difference in nonparametric regression," Computational Statistics, Springer, vol. 32(3), pages 1047-1063, September.
    12. Golubev, Georgi & Härdle, Wolfgang, 2000. "On adaptive estimation in partial linear models," SFB 373 Discussion Papers 2000,21, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    13. Peter Hall & Ingrid Van Keilegom, 2003. "Using difference‐based methods for inference in nonparametric regression with time series errors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 443-456, May.
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