Non- and Semi-Parametric Maximum Likelihood Estimators and the von Mises Method. Part 1

摘要

The approach to von Mises derivatives based on compact differentiation due to Reeds (1976) is introduced, and it is shown how nonparametric 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. Examples show that it usually not possible to base consistency and asymptotic normality theorems on the implicit function theorem.