Estimation after selection from bivariate normal population using LINEX loss function
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Let π_1 and π_2 be two independent populations, where the population π_i follows a bivariate normal distribution with unknown mean vector θ^(i) and common known variance-covariance matrix Σ, i=1,2. The present paper is focused on estimating a characteristic θ_y^S of the selected bivariate normal population, using a LINEX loss function. A natural selection rule is used for achieving the aim of selecting the best bivariate normal population. Some natural-type estimators and Bayes estimator (using a conjugate prior) of θ_y^S are presented. An admissible subclass of equivariant estimators, using the LINEX loss function, is obtained. Further, a sufficient condition for improving the competing estimators of θ_y^S is derived. Using this sufficient condition, several estimators improving upon the proposed natural estimators are obtained. Further, a real data example is provided for illustration purpose. Finally, a comparative study on the competing estimators of θ_y^S is carried-out using simulation.
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