Abstract
The general Gauss-Markov model M = { Y, X, β, σ 2 V} with linear restrictions Rβ = r , denoted by M r , is compared with the model M with implied linear restrictions ARβ = Ar , denoted by M ∗ r . Necessary and sufficient conditions are derived under which (i) the consistency condition, (ii) the minimum dispersion linear unbiased estimator of a given vector of estimable parametric functions of β , and (iii) the minimum norm quadratic unbiased estimator of σ 2 for the two restricted models M r and M ∗ r are identical. The results obtained cover those concerning comparison of the restricted model M r to the unrestricted model M.
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