Simultaneous Estimation of Parameters in Different Linear Models and Applications to Biometric Problems

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Abstract
Empirical Bayes procedure is employed in simultaneous estimation of vector parameters from a number of Gauss-Markoff linear models. It is shown that with respect to quadratic loss function, empirical Bayes estimators are better than least squares estimators. While estimating the parameter for a particular linear model, a suggestion has been made for distinguishing between the loss due to decision maker and the loss due to individual. A method has been proposed but not fully studied to achieve balance between the two losses. Finally the problem of predicting future observations in a linear model has been considered.

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