Rates of convergence for the pre-asymptotic substitution bandwidth selector

Jianqing Fan; Li Shan Huang

doi:10.1016/S0167-7152(98)00271-5

Rates of convergence for the pre-asymptotic substitution bandwidth selector

Jianqing Fan, Li Shan Huang

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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.

Original language	English (US)
Pages (from-to)	309-316
Number of pages	8
Journal	Statistics and Probability Letters
Volume	43
Issue number	3
DOIs	https://doi.org/10.1016/S0167-7152(98)00271-5
State	Published - Jul 1 1999
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Bandwidth selection
Convergence rate
Kernel density estimation
Local polynomial regression

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10.1016/S0167-7152(98)00271-5

Cite this

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title = "Rates of convergence for the pre-asymptotic substitution bandwidth selector",

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.",

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T1 - Rates of convergence for the pre-asymptotic substitution bandwidth selector

AU - Fan, Jianqing

AU - Huang, Li Shan

PY - 1999/7/1

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N2 - 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.

AB - 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.

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KW - Kernel density estimation

KW - Local polynomial regression

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Rates of convergence for the pre-asymptotic substitution bandwidth selector

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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