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A NONPARAMETRIC REGRESSION ESTIMATOR THAT ADAPTS TO ERROR DISTRIBUTION OF UNKNOWN FORM

Published online by Cambridge University Press:  05 April 2007

Oliver Linton  and
Zhijie Xiao
Oliver Linton
Affiliation:
London School of Economics
Zhijie Xiao
Affiliation:
Boston College
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Abstract

We propose a new kernel estimator for nonparametric regression with unknown error distribution. We show that the proposed estimator is adaptive in the sense that it is asymptotically equivalent to the infeasible local likelihood estimator (Staniswalis, 1989, Journal of the American Statistical Association 84, 276–283; Fan, Farmen, and Gijbels, 1998, Journal of the Royal Statistical Society, Series B 60, 591–608; and Fan and Chen, 1999, Journal of the Royal Statistical Society, Series B 61, 927–943), which requires knowledge of the error distribution. Hence, our estimator improves on standard nonparametric kernel estimators when the error distribution is not normal. A Monte Carlo experiment is conducted to investigate the finite-sample performance of our procedure.We thank Yuichi Kitamura, Yanqin Fan, Joel Horowitz, Roger Koenker, Jens Perch Nielsen, Peter Phillips, Peter Robinson, Tom Rothenberg, and two referees for helpful comments. Financial support from the NSF and the ESRC (UK) is gratefully acknowledged.

Type
Research Article
Information
Econometric Theory , Volume 23 , Issue 3 , June 2007 , pp. 371 - 413
Copyright
© 2007 Cambridge University Press

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