Preliminary test and Stein estimations in simultaneous linear equations

Abstract In modeling of an economic system, there may occur some stochastic constraints, that can cause some changes in the estimators and their respective behaviors. In this approach we formulate the simultaneous equation models into the problem of estimating the regression parameters of a multiple regression model, under elliptical errors. We define five different sorts of estimators for the vector-parameter. Their exact risk expressions are also derived under the balanced loss function. Comparisons are then made to clarify the performance of the proposed estimators. It is shown that the shrinkage factor of the Stein estimator is robust with respect to departures from normality assumption.

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