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NONPARAMETRIC ESTIMATION OF HOMOGENEOUS FUNCTIONS

Published online by Cambridge University Press:  06 June 2003

Gautam Tripathi  and
Woocheol Kim
Gautam Tripathi
Affiliation:
University of Wisconsin-Madison
Woocheol Kim
Affiliation:
Humboldt-Universität zu Berlin
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Abstract

Consider the regression , where and the exact functional form of f is unknown, although we do know that f is homogeneous of known degree r. Using a local linear approach, we examine two ways of nonparametrically estimating f: (i) a “direct” approach and (ii) a “projection based” approach. We show that depending upon the nature of the conditional variance , one approach may be asymptotically better than the other. Results of a small simulation experiment are presented to support our findings.We thank Don Andrews and an anonymous referee for comments that greatly improved this paper. The first author thanks Professor Wolfgang Härdle for hospitality at the Institute of Statistics and Econometrics, Humboldt University, Berlin, where part of this research was carried out. Financial support to the first author from Sonderforschungsbereich 373 (“Quantifikation und Simulation Ökonomischer Prozesse”) and the NSF via grants SES-0111917 and SES-0214081 is also gratefully acknowledged.

Type
Research Article
Information
Econometric Theory , Volume 19 , Issue 4 , August 2003 , pp. 640 - 663
Copyright
© 2003 Cambridge University Press

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