On maximum likelihood estimation in infinite dimensional parameter spaces. (English) Zbl 0732.62026

The authors study the rate of convergence and asymptotic efficiency of an approximate maximum likelihood estimator for estimating smooth functionals of an infinite-dimensional parameter under some regularity conditions. The rate is governed by the size of the space of score functions measured by an entropy index. The theory is illustrated by examples on density estimation, conditionally exponential family models and transformation models. Possible applications to semiparametric models are discussed.


62F12 Asymptotic properties of parametric estimators
62G20 Asymptotic properties of nonparametric inference
62G07 Density estimation
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