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December, 1988 Estimating a Real Parameter in a Class of Semiparametric Models
A. W. van der Vaart
Ann. Statist. 16(4): 1450-1474 (December, 1988). DOI: 10.1214/aos/1176351048


We study semiparametric models where for a fixed value of the finite-dimensional parameter there exists a sufficient statistic for the nuisance parameter. An asymptotically normal sequence of estimators for the parametric component is constructed, which is efficient under the assumption that projecting on the set of nuisance scores is equivalent to taking conditional expectations given the sufficient statistic. The latter property is checked for a number of examples, in particular for mixture models. We discuss the relation of our approach to conditional maximum likelihood estimation.


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A. W. van der Vaart. "Estimating a Real Parameter in a Class of Semiparametric Models." Ann. Statist. 16 (4) 1450 - 1474, December, 1988.


Published: December, 1988
First available in Project Euclid: 12 April 2007

zbMATH: 0665.62034
MathSciNet: MR964933
Digital Object Identifier: 10.1214/aos/1176351048

Primary: 62F12
Secondary: 62F10 , 62F35 , 62G05 , 62G20

Keywords: Adaptation , asymptotic efficient estimation , conditional maximum likelihood , mixture model , Semiparametric model

Rights: Copyright © 1988 Institute of Mathematical Statistics


Vol.16 • No. 4 • December, 1988
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