Estimation of $p, p \geq 3$, location parameters of a distribution of a p-dimensional random vector $\mathsf{X}$ is considered under quadratic loss. Explicit estimators which are better than the best invariant one are given for a sign-invariantly distributed random vector $\mathsf{X}$. The results depend only on the second and the third moments of $|| \mathsf{X} - \theta ||$. The generalizations to concave loss functions and to n observations are also considered. Additionally, if the scale is unknown, we investigate the estimators of the location parameters when the observation contains a residual vector.
@article{1069362397,
author = {Xu, Jian-Lun},
title = {Simultaneous estimation of location parameters for sign-invariant distributions},
journal = {Ann. Statist.},
volume = {25},
number = {6},
year = {1997},
pages = { 2259-2272},
language = {en},
url = {http://dml.mathdoc.fr/item/1069362397}
}
Xu, Jian-Lun. Simultaneous estimation of location parameters for sign-invariant distributions. Ann. Statist., Tome 25 (1997) no. 6, pp. 2259-2272. http://gdmltest.u-ga.fr/item/1069362397/