Shrinkage estimation of non-negative mean vector with unknown covariance under balance loss

Abstract

Abstract Parameter estimation in multivariate analysis is important, particularly when parameter space is restricted. Among different methods, the shrinkage estimation is of interest. In this article we consider the problem of estimating the p-dimensional mean vector in spherically symmetric models. A dominant class of Baranchik-type shrinkage estimators is developed that outperforms the natural estimator under the balance loss function, when the mean vector is restricted to lie in a non-negative hyperplane. In our study, the components of the diagonal covariance matrix are assumed to be unknown. The performance evaluation of the proposed class of estimators is checked through a simulation study along with a real data analysis.

Keywords

• Baranchik-type estimator
• Balance loss function
• Restricted estimator
• Shrinkage estimator
• Spherical distribution