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NONPARAMETRIC ESTIMATION OF REGRESSION FUNCTIONS WITH DISCRETE REGRESSORS

Published online by Cambridge University Press:  01 February 2009

Desheng Ouyang ,
Qi Li  and
Jeffrey S. Racine
Desheng Ouyang
Affiliation:
Shanghai University of Finance and Economics
Qi Li
Affiliation:
Texas A&M University and Tsinghua University
Jeffrey S. Racine*
Affiliation:
McMaster University
*
*Address correspondence to Jeffrey S. Racine, Department of Economics, McMaster University, Graduate Program in Statistics, McMaster University, Hamilton, ON L8S 4M4, Canada; e-mail: racinej@mcmaster.ca.
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Abstract

We consider the problem of estimating a nonparametric regression model containing categorical regressors only. We investigate the theoretical properties of least squares cross-validated smoothing parameter selection, establish the rate of convergence (to zero) of the smoothing parameters for relevant regressors, and show that there is a high probability that the smoothing parameters for irrelevant regressors converge to their upper bound values, thereby automatically smoothing out the irrelevant regressors. A small-scale simulation study shows that the proposed cross-validation-based estimator performs well in finite-sample settings.

Type
ARTICLES
Information
Econometric Theory , Volume 25 , Issue 1 , February 2009 , pp. 1 - 42
Copyright
Copyright © Cambridge University Press 2009

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