Theory and Methods of Statistics

10

Statistical Functionals and Their Use in Robust Estimation

Abstract

A statistical functional $T\left(F\right)$ is a real-valued function of a cdf F ∈ F₀, of which $T\left(F_n\right)$ is a natural estimate based on the edf F_n of a random sample of size n from F. Therefore, the behavior of $T\left(F_n\right)-T\left(F\right)$ is of interest. Analogous to the expansion of $\sqrt{n}\left[T\left({\widehat{\theta }}_n\right)-T\left(\theta \right)\right]$ in the parametric setting, ...