On an Identity Derived from Unbiasedness in Linear Models

Abstract

Difficulties associated with deriving AX = X as a necessary condition from Ay + c being an unbiased estimator of Xβ are discussed in terms of the linear model y ∼ (Xβ, V). We demonstrate two instances in which AX = X and c = 0 are not necessary conditions but then argue that these can be ignored in practice. Excluding these possibilities leads to AX = X and c = 0 being necessary.

Key Words:

• Estimable parameter constraints
• Singular dispersion matrix
• Nonlinear estimators