ADDING REGRESSORS TO OBTAIN EFFICIENCY
在异方差条件下,添加与现有回归变量正交的无关变量,可以使得普通最小二乘估计达到广义最小二乘估计的渐近方差。
It is well known that in standard linear regression models with independent and identically distributed data and homoskedasticity, adding “irrelevant regressors” hurts (asymptotic) efficiency unless such irrelevant regressors are orthogonal to the remaining regressors. But we have found that under (conditional) heteroskedasticity “irrelevant regressors” can always be found such that one can achieve the asymptotic variance of the generalized least squares estimator by adding the “irrelevant regressors” to the model.