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Simulation-based two-stage estimation for multiple nonparametric regression

Author

Listed:
  • Lin, Lu
  • Zhang, Qi
  • Li, Feng
  • Cui, Xia

Abstract

To reduce the curse of dimensionality arising from nonparametric estimation procedures for multiple nonparametric regression, in this paper we suggest a simulation-based two-stage estimation. We first introduce a simulation-based method to decompose the multiple nonparametric regression into two parts. The first part can be estimated with the parametric convergence rate and the second part is small enough so that it can be approximated by orthogonal basis functions with a small trade-off parameter. Then the linear combination of the first and second step estimators results in a two-stage estimator for the multiple regression function. Our method does not need any specified structural assumption on the regression function and it is proved that the newly proposed estimation is always consistent even if the trade-off parameter is designed to be small. Thus when the common nonparametric estimator such as local linear smoothing collapses because of the curse of dimensionality, our estimator still works well.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:3:p:1367-1378
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    References listed on IDEAS

    as
    1. 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.
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