A central limit theorem for multivariate generalized trimmed $k$-means

Abstract

A central limit theorem for generalized trimmed $k$-means is obtained in a very general framework that covers the multivariate setting, general penalty functions and general $k \geq 1$. Several applications, including the location estimator case $(k = 1)$ for elliptical distributions and the construction of multivariate (not necessarily connected) tolerance zones, are also given.