# Convergence in distribution of minimum-distance estimators

Bolthausen, E (1977). Convergence in distribution of minimum-distance estimators. Metrika, 24(4):215-227.

## Abstract

It is shown that (under some regularity conditions) minimum distance estimators for a (possibly multidimensional) real parameter of a family of univariate continuous distribution functions have an asymptotic distribution. If the distance is derived from the mean-square norm it is proved that the asymptotic distribution is normal. Weak convergence of empirical distribution to the Brownian bridge is the essential tool for the proof.

It is shown that (under some regularity conditions) minimum distance estimators for a (possibly multidimensional) real parameter of a family of univariate continuous distribution functions have an asymptotic distribution. If the distance is derived from the mean-square norm it is proved that the asymptotic distribution is normal. Weak convergence of empirical distribution to the Brownian bridge is the essential tool for the proof.