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A PUZZLING PHENOMENON IN SEMIPARAMETRIC ESTIMATION PROBLEMS WITH INFINITE-DIMENSIONAL NUISANCE PARAMETERS

Published online by Cambridge University Press:  18 July 2008

Kohtaro Hitomi ,
Yoshihiko Nishiyama  and
Ryo Okui
Kohtaro Hitomi
Affiliation:
Kyoto Institute of Technology
Yoshihiko Nishiyama
Affiliation:
Kyoto University
Ryo Okui*
Affiliation:
Hong Kong University of Science and Technology
*
Address correspondence to Ryo Okui, Department of Economics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong; e-mail: okui@ust.hk
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Abstract

This note considers a puzzling phenomenon that is observed in some semiparametric estimation problems. In some cases, using estimated values of the nuisance parameters provides a more efficient estimator for the parameters of interest than does using the true values. This phenomenon takes place even in cases of semi-nonparametric models in which the nuisance parameters are infinite-dimensional and cannot be estimated at the parametric rate. We examine the structure and present the necessary and sufficient condition for the occurrence of this puzzle. We also provide a simple sufficient condition. It shows that the puzzle occurs when the term accounting for the effect of estimation of nuisance parameters is included in the tangent space. This condition is often satisfied when the estimating equation does not bring any restriction on the form of the nuisance parameters. Our simple sufficient condition can be applied to many important estimators.

Type
Notes and Problems
Information
Econometric Theory , Volume 24 , Issue 6 , December 2008 , pp. 1717 - 1728
Copyright
Copyright © Cambridge University Press 2008

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