ABSTRACT
In the regression model https://www.w3.org/1998/Math/MathML"> y = X β + ε , E { ε } = 0 , E { ε ε ′ } = σ 2 Ω , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203180754/695bd69b-d1f9-4baf-8f3a-2907edb27a88/content/math_456_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> where X is n × k of rank k, one may wish to obtain the minimum-variance conditionally unbiased affine estimator of β subject to a set of linear restrictions https://www.w3.org/1998/Math/MathML"> Ψ β = α , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203180754/695bd69b-d1f9-4baf-8f3a-2907edb27a88/content/math_457_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> where Ψ is r × k of rank r. Or one may wish to test the null hypothesis that (4.1.2) is true, against the alternative hypothesis that Ψβ ≠ α, on the assumption that ε ~ N(0,σ 2Ω), that is, that ε has the multivariate normal distribution with mean vector 0 and variance matrix σ 2Ω (Ω known).
