NONPARAMETRIC ESTIMATION OF HOMOGENEOUS FUNCTIONS

Gautam Tripathi and Woocheol Kim

Econometric Theory, 2003, vol. 19, issue 04, pages 640-663

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 H rdle 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 konomischer Prozesse ) and the NSF via grants SES-0111917 and SES-0214081 is also gratefully acknowledged.

Date: 2003

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