The Annals of Statistics

Estimating a Real Parameter in a Class of Semiparametric Models

A. W. van der Vaart

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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.

Article information

Ann. Statist., Volume 16, Number 4 (1988), 1450-1474.

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62F12: Asymptotic properties of estimators
Secondary: 62F35: Robustness and adaptive procedures 62F10: Point estimation 62G05: Estimation 62G20: Asymptotic properties

Semiparametric model asymptotic efficient estimation adaptation mixture model conditional maximum likelihood


van der Vaart, A. W. Estimating a Real Parameter in a Class of Semiparametric Models. Ann. Statist. 16 (1988), no. 4, 1450--1474. doi:10.1214/aos/1176351048.

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