## The Annals of Statistics

### Minimax Estimation of Location Parameters for Spherically Symmetric Distributions with Concave Loss

#### Abstract

For $p \geqslant 4$ and one observation $X$ on a $p$-dimensional spherically symmetric distribution, minimax estimators of $\theta$ whose risks are smaller than the risk of $X$ (the best invariant estimator) are found when the loss is a nondecreasing concave function of quadratic loss. For $n$ observations $X_1, X_2, \cdots, X_n$, we have classes of minimax estimators which are better than the usual procedures, such as the best invariant estimator, $\bar{X}$, or a maximum likelihood estimator.

#### Article information

Source
Ann. Statist., Volume 8, Number 2 (1980), 279-284.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176344953

Digital Object Identifier
doi:10.1214/aos/1176344953

Mathematical Reviews number (MathSciNet)
MR560729

Zentralblatt MATH identifier
0432.62008

JSTOR