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Simultaneous estimation of location parameters for sign-invariant distributions. (English) Zbl 0881.62060

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.

MSC:

62H12 Estimation in multivariate analysis
62C99 Statistical decision theory
62F10 Point estimation
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