Asymptotic normality of multivariate trimmed means

We prove the asymptotic normality of the trimmed mean, obtained by deleting the data which is further away from a parameter of location [theta]n. To get this trimmed mean, equivariant by rotations, dilations and translations, we choose [theta]n in a class of multivariate parameters of location, which are equivariant by these transformations. Given the data X1, ... , Xn, we take as [theta]n, the value such that where h is a nondecreasing function and x is the Euclidean distance in Bd. This estimator [theta]n is equivariant by rotations and translations. If h(x) = xp, [theta]n is also equivariant by dilations.