We consider the problem of estimating k coefficients of interest in a linear regression model when the (k + 1)st coefficient is of no interest. The traditional pretest estimator is a two-step estimator of the coefficients of interest based on a t-test for the (k + 1)st coefficient. We study the behaviorof this estimator. Questions of admissibility, risk, and regret are addressed.
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Jan R. Magnus (2000) studied this question.
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