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Article: Illustrating the Gauss-Markov theorem.
- Article from:
- The American Statistician
- Article date:
- August 1, 1994
CopyrightCOPYRIGHT 1994 American Statistical Association. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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1. SIMPLE EXAMPLE
A thorough course in regression analysis will include a discussion of the well-known Gauss-Markov theorem (e.g., Rao 1973). In the context of an intercept-only model, the theorem states that if
[Y.sub.i] = [[beta].sub.0] + [[epsilon].sub.i] (i = 1 , ..., n),
and the [[epsilon].sub.i] are uncorrelated with zero mean and (common) variance [[sigma].sup.2], then the best linear unbiased estimator (BLUE) for [[beta].sub.0] is [[beta].sub.0] = [bar]Y, the sample mean of the [Y.sub.i]. The estimator [[beta].sub.0] is "best" in the sense it has the smallest variance, namely [[sigma].sup.2]/n, among all possible linear unbiased ...