The Annals of Statistics

Variable Selection in Nonparametric Regression with Continuous Covariates

Ping Zhang

Full-text: Open access

Abstract

In a nonparametric regression setup where the covariates are continuous, the problem of estimating the number of covariates will be discussed in this paper. The kernel method is used to estimate the regression function and the selection criterion is based on minimizing the cross-validation estimate of the mean squared prediction error. We consider choosing both the bandwidth and the number of covariates based on the data. Unlike the case of linear regression, it turns out that the selection is consistent and efficient even when the true model has only a finite number of covariates. In addition, we also observe the curse of dimensionality at work.

Article information

Source
Ann. Statist. Volume 19, Number 4 (1991), 1869-1882.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176348375

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aos/1176348375

Mathematical Reviews number (MathSciNet)
MR1135153

Zentralblatt MATH identifier
0738.62051

Subjects
Primary: 62G05: Estimation
Secondary: 62J99: None of the above, but in this section

Keywords
Cross-validation kernel estimate model selection

Citation

Zhang, Ping. Variable Selection in Nonparametric Regression with Continuous Covariates. Ann. Statist. 19 (1991), no. 4, 1869--1882. doi:10.1214/aos/1176348375. http://projecteuclid.org/euclid.aos/1176348375.


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