Estimating a Real Parameter in a Class of Semiparametric Models

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 project...

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Bibliographic Details
Published in:The Annals of statistics 1988-12, Vol.16 (4), p.1450-1474
Main Author: van der Vaart, A. W.
Format: Article
Language:English
Subjects:
62F10
62F12
62F35
62G05
62G20
adaptation
asymptotic efficient estimation
conditional maximum likelihood
Consistent estimators
Density
Estimators
Exact sciences and technology
Induced substructures
Lebesgue measures
Mathematical functions
Mathematics
Maximum likelihood estimation
Maximum likelihood estimators
mixture model
Parametric inference
Point estimators
Probability and statistics
Sciences and techniques of general use
Semiparametric model
Semiparametric modeling
Statistics
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Description
Summary: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.
ISSN:0090-5364
2168-8966
DOI:10.1214/aos/1176351048