Efficiency. of infinite dimensional M- estimators |
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Authors: | A W van der Vaart |
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Institution: | Department of Mathematics and Computer Science, Free University, De Boelelaan 1081a. 1081 HV Amsterdam, The Netherlands |
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Abstract: | It is well-known that maximum likelihood estimators are asymptotically normal with covariance equal to the inverse Fisher information in smooth, finite dimensional parametric models. Thus they are asymptotically efficient. A similar phenomenon has been observed for certain infinite dimensional parameter spaces. We give a simple proof of efficiency, starting from a theorem on asymptotic normality of infinite dimensional M -estimators. The proof avoids the explicit calculation of the Fisher information. We also address Hadamard differentiability of the corresponding M -functionals. |
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Keywords: | M-estimator asymptotic efficiency semiparametric model maximum likelihood |
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