Year: 1986
Type: other
Abstract: After introducing the approach to von Mises derivatives based on compact differentiation due to REEDS (1976), we show how non-parametric maximum likelihood estimators can often be defined by solving infinite dimensional score equations.Each component of the score equation corresponds to the derivative of the log likelihood for a one-dimensional parametric submodel.By means of examples we show that it usually is not possible to base consistency and asymptotic normality theorems on the implicit function theorem.However (in Part II) we show for a particular class of models, that once consistency (in a rather strong sense) has been established by other means, asymptotic normality and efficiency of the nonparametric maximum likelihood estimator can be established by the von Mises method.
Author: Richard D. Gill
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2008831573