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.
Highlights
Shrinkage estimation is a method to improve a raw estimator in some sense, by combining it with other information
Mean vector parameter estimation is an important problem in the context of shrinkage estimation, specially when some components of location parameter are restricted to be situated in a specific space
5 Air pollution data we further investigate the superior performance of the Baranchik-type shrinkage estimator compared to the natural estimator
Summary
Shrinkage estimation is a method to improve a raw estimator in some sense, by combining it with other information. We develop the approach of Fourdrinier et al [7], in which they estimated location parameter-vector when some components are non-negative, for unknown covariance matrix under balance loss function. Proof Since 0 ≤ r(·) ≤ 1 is a non-negative, differentiable and concave function by Lemma 3.3, we have r (·) ≥ 0. The shrinkage estimator X + γq(X) + g(X, S) dominates the natural estimator X + γq(X) under the BEL(δ0(i)), if the following conditions hold: For. Proof The proof is similar to that of Theorem 3.1.
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