Efficient estimation in single-index regression

Michel Delecroix, Wolfgang Härdle and Marian Hristache

No 1997,37, SFB 373 Discussion Papers from Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes

Abstract: Semiparametric single-index regression involves an unknown finite dimensional parameter and an unknown (link) function. We consider estimation of the parameter via the pseudo maximum likelihood method. For this purpose we estimate the conditional density of the response given a candidate index and maximize the obtained likelihood. We show that this technique of adaptation yields an asymptotically efficient estimator : it has minimal variance among all estimators.

Date: 1997
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