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误设回归模型中线性约束预检验的最优检验水平AI 解读

When the choice of estimator for the coefficients in a linear regression model is determined by the outcome of a prior test of the validity of restrictions on the model, it is well known that a minimax (risk) regret criterion leads to the simple rule that the optimal critical value for the preliminary test is approximately two in value, regardless of the degrees of freedom. We show that this result no longer holds in the (likely) event that relevant regressors are excluded…

线性回归误差方差的预检验估计AI 解读

We derive exact finite-sample expressions for the biases and risks of several common pretest estimators of the scale parameter in the linear regression model. These estimators are associated with least squares, maximum likelihood and minimum mean squared error component estimators. Of these three criteria, the last is found to be superior (in terms of risk under quadratic loss) when pretesting in typical situations.