Abstract
AbstractConsider the two linear regression models of Yij on Xij, namely Yij = βio + βil Xij + εij,j = 1,2,…,ni, i = 1,2, where εij are assumed to be normally distributed with zero mean and common unknown variance σ2. The estimated value of a mean of Y1 for a given value of X1 is made to depend on a preliminary test of significance of the hypothesis β11 = β21. The bias and the mean square error of the estimator for the conditional mean of Y1 are given. The relative efficiency of the estimator to the usual estimator is computed and is used to determine a proper choice of the significance level of the preliminary test.
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