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Rates of convergence for the pre-asymptotic substitution bandwidth selector

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  • Fan, Jianqing
  • Huang, Li-Shan

Abstract

An effective bandwidth selection method for local linear regression is proposed in Fan and Gijbels [1995, J. Roy. Statist. Soc. Ser. B, 57, 371-394]. The method is based on the idea of the pre-asymptotic substitution and has been tested extensively. This paper investigates the rate of convergence of this method. In particular, we show that the relative rate of convergence is of order n-2/7 if the locally cubic fitting is used in the pilot stage, and the rate of convergence is n-2/5 when the local polynomial of degree 5 is used in the pilot fitting. The study also reveals a marked difference between the bandwidth selection for nonparametric regression and that for density estimation: The plug-in approach for the latter case can admit the root-n rate of convergence while for the former case the best rate is of order n-2/5.

Suggested Citation

  • Fan, Jianqing & Huang, Li-Shan, 1999. "Rates of convergence for the pre-asymptotic substitution bandwidth selector," Statistics & Probability Letters, Elsevier, vol. 43(3), pages 309-316, July.
    • Handle: RePEc:eee:stapro:v:43:y:1999:i:3:p:309-316
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