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On an Identity Derived from Unbiasedness in Linear Models

C. E. McCulloch and S. R. Searle
The American Statistician
Vol. 49, No. 1 (Feb., 1995), pp. 39-42
DOI: 10.2307/2684809
Stable URL: http://www.jstor.org/stable/2684809
Page Count: 4
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On an Identity Derived from Unbiasedness in Linear Models
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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.

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