Abstract
Lehmann ( Theory of Point Estimation , 1983, Wiley, New York) discusses the problem of marginal equivariant estimation of the parameters of a location-scale model. In this paper, we develop the procedure of simultaneous equivariant estimation of the parameters and extend the results discussed in Lehmann ( Theory of Point Estimation , 1983, Wiley, New York). The vector minimum risk equivariant (MRE) estimator is characterized under certain conditions. By considering quadratic-type loss function ( Zacks, Theory of Statistical Inference , 1971, p. 102, Wiley, New York), a characterization and also uniqueness of the vector MRE estimator is obtained. Two examples are discussed to illustrate the technique involved.
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