PMSE PERFORMANCE OF THE BIASED ESTIMATORS IN A LINEAR REGRESSION MODEL WHEN RELEVANT REGRESSORS ARE OMITTED
研究了线性回归模型中遗漏相关解释变量时，四种估计量的预测均方误差，发现正部分Stein规则估计量和调整最小均方误差估计量优于普通最小二乘估计量。
In this paper, we consider a linear regression model when relevant regressors are omitted. We derive the explicit formulae for the predictive mean squared errors (PMSEs) of the Stein-rule (SR) estimator, the positive-part Stein-rule (PSR) estimator, the minimum mean squared error (MMSE) estimator, and the adjusted minimum mean squared error (AMMSE) estimator. It is shown analytically that the PSR estimator dominates the SR estimator in terms of PMSE even when there are omitted relevant regressors. Also, our numerical results show that the PSR estimator and the AMMSE estimator have much smaller PMSEs than the ordinary least squares estimator even when the relevant regressors are omitted.