Xu, Jian-Lun Simultaneous estimation of location parameters for sign-invariant distributions. (English) Zbl 0881.62060 Ann. Stat. 25, No. 5, 2259-2272 (1997). Summary: Estimation of \(p\), \(p\geq 3\), location parameters of a distribution of a \(p\)-dimensional random vector \({\mathbf X}\) is considered under quadratic loss. Explicit estimators which are better than the best invariant one are given for a sign-invariantly distributed random vector \({\mathbf X}\). The results depend only on the second and the third moments of \(|{\mathbf X} -\theta|\). 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. Cited in 2 Documents MSC: 62H12 Estimation in multivariate analysis 62C99 Statistical decision theory 62F10 Point estimation Keywords:simultaneous estimation; location parameters; sign-invariant distributions; risk function; quadratic loss × Cite Format Result Cite Review PDF Full Text: DOI