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Stable and bias-corrected estimation for nonparametric regression models

Author

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  • Lu Lin
  • Feng Li

Abstract

It is well known that in nonparametric regression setting, the common kernel estimators are sensitive to bandwidth and can not achieve a satisfactory convergence rate, especially for multivariate cases. To improve nonparametric estimation in the sense of both selection of bandwidth and convergence rate, this paper proposes a two-stage (or three-stage) regression estimation by combining nonparametric regression with parametric regression. The optimal design conditions, including the optimal bandwidth, are obtained. The newly proposed estimator has a simple structure and can achieve a smaller mean square error without use of the higher order kernel. Even if the prior selections of nonparametric estimation are not optimal (i.e. the smooth parameter is not optimally chosen), the new two-stage estimator still has a satisfactory convergence rate. This means that the newly proposed estimator is robust to the selection of bandwidth and then is a practical method. This new method is also suitable for general nonparametric regression models regardless of the dimension of explanatory variable and the structure assumption on regression function.

Suggested Citation

  • Lu Lin & Feng Li, 2008. "Stable and bias-corrected estimation for nonparametric regression models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(4), pages 283-303.
    • Handle: RePEc:taf:gnstxx:v:20:y:2008:i:4:p:283-303
    DOI: 10.1080/10485250802018253
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    References listed on IDEAS

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    1. Tiejun Tong & Yuedong Wang, 2005. "Estimating residual variance in nonparametric regression using least squares," Biometrika, Biometrika Trust, vol. 92(4), pages 821-830, December.
    2. Gordon, Louis & Olshen, Richard A., 1980. "Consistent nonparametric regression from recursive partitioning schemes," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 611-627, December.
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    Cited by:

    1. Giordano, Francesco & Parrella, Maria Lucia, 2016. "Bias-corrected inference for multivariate nonparametric regression: Model selection and oracle property," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 71-93.
    2. Francesco Giordano & Maria Lucia Parrella, 2014. "Bias-corrected inference for multivariate nonparametric regression: model selection and oracle property," Working Papers 3_232, Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Salerno.
    3. Lu Lin & Feng Li, 2023. "Global debiased DC estimations for biased estimators via pro forma regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 726-758, June.
    4. Lin, Lu & Zhang, Qi & Li, Feng & Cui, Xia, 2011. "Simulation-based two-stage estimation for multiple nonparametric regression," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1367-1378, March.

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