The frisch-waugh theorem and generalized least squares
研究了非球形扰动下线性回归模型中，使用辅助回归残差进行广义最小二乘估计的条件，指出伪GLS与真实GLS相等的条件常被违反，但弗里施-沃定理在有效估计下仍成立。
We discuss the standard linear regression model with nonspherical disturbances, where some regressors are annihilated by considering only the residuals from an auxiliary regression, and where, analogous to the Frisch-Waugh procedure, the original GLS procedure is applied to the transformed data. We call this procedure pseudo-GLS and give conditions for pseudo-GL5 to be equal to genuine GLS. We also show via examples that these conditions are often violated in empirical applications, and that the Frisch-Waugh Theorem still “works” with nonspherical disturbances if efficient estimation is applied to both the original and the transformed data.