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October 1997 Simultaneous estimation of location parameters for sign-invariant distributions
Jian-Lun Xu
Ann. Statist. 25(5): 2259-2272 (October 1997). DOI: 10.1214/aos/1069362397


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.


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Jian-Lun Xu. "Simultaneous estimation of location parameters for sign-invariant distributions." Ann. Statist. 25 (5) 2259 - 2272, October 1997.


Published: October 1997
First available in Project Euclid: 20 November 2003

zbMATH: 0881.62060
MathSciNet: MR1474093
Digital Object Identifier: 10.1214/aos/1069362397

Primary: 62C99
Secondary: 62F10 , 62H12

Keywords: location parameters , quadratic loss , risk function , sign-invariant distributions , simultaneous estimation

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 5 • October 1997
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