Abstract
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.
Highlights
Shrinkage estimation is a method that a naıve or target estimator is improved, in some sense, by combining it with other information
Innovative approaches in the context of restricted models continued by the work of Marchand and Strawderman [23] for location families with densities of the form f0(x − θ). They dealt with a lower bound constraint of the form θ > a, while Marchand and Perron [22] extended the result for spherically symmetric distribution under constrained parameter space Θ(m) = {θ ∈ Rp : ∥θ∥ ≤ m for some fixed m > 0}
Kortbi and Marchand [17] exhibited a truncated linear estimator for the constraint ∥θ∥ ≤ m, in the multivariate normal model and Marchand and Strawderman [24] developed a unified approach for minimax estimation for restricted parameter space
Summary
Shrinkage estimation is a method that a naıve or target estimator is improved, in some sense, by combining it with other information. Innovative approaches in the context of restricted models continued by the work of Marchand and Strawderman [23] for location families with densities of the form f0(x − θ) They dealt with a lower bound constraint of the form θ > a, while Marchand and Perron [22] extended the result for spherically symmetric distribution under constrained parameter space Θ(m) = {θ ∈ Rp : ∥θ∥ ≤ m for some fixed m > 0}. Kortbi and Marchand [17] exhibited a truncated linear estimator for the constraint ∥θ∥ ≤ m, in the multivariate normal model and Marchand and Strawderman [24] developed a unified approach for minimax estimation for restricted parameter space.
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