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The paper considers the estimation of the slope parameter for k ≥ 3, in a general linear model. A class of James Stein estimators is proposed and is compared with the least squares estimator under an appropriate stopping rule. It is shown that the sequential James Stein estimator dominates the sequential least squares estimator. Furthermore, under mild regularity conditions, a second order asymptotic risk expansion for the sequential James-Stein estimator is obtained.
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