The Location Parameter Estimation of Spherically Distributions with Known Covariance Matrices

This paper presents shrinkage estimators of the location parameter vector for spherically symmetric distributions. We suppose that the mean vector is non-negative constraint and the components of diagonal covariance matrix is known. We compared the present estimator with natural estimator by using risk function. We show that when the covariance matrices are known, under the balance error loss function, shrinkage estimator has the smaller risk than the natural estimator. Simulation results are provided to examine the shrinkage estimators.