The exact risk performance of a pre-test estimator in a heteroskedastic linear regression model under the balanced loss function
研究了在平衡损失函数下，对回归系数进行同方差性预检验后使用的预检验估计量的风险，发现当临界值为1时该估计量优于两阶段Aitken估计量，且当拟合优度比估计精度更重要时，普通最小二乘估计量可能更优。
We examine the risk of a pre-test estimator for regression coefficients after a pre-test for homoskedasticity under the Balanced Loss Function (BLF). We show analytically that the two stage Aitken estimator is dominated by the pre-test estimator with the critical value of unity, even if the BLF is used. We also show numerically that both the two stage Aitken estimator and the pre-test estimator can be dominated by the ordinary least squares estimator when “goodness of fit” is regarded as more important than precision of estimation.