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Gauss–Markov 模型下的实验合并AI 解读

Consider two experiments with homoscedastic models E(Yi ) = Xi θ + Zi ψ, V(Yi ) = σ2 Ini (i = 1, 2). The matrix gi = X'i (Ini — Zi (Z'iZi )Xi can be called the information matrix of linear estimable functions of θ for experiment i. The information matrix g for the combined data (Y 1, Y 2) may be similarly defined. A proof of g ⩾ g 1 + g 2 (⩾ in the sense of nonnegative definiteness) is given, and equality is interpreted. g = g 1 + g 2 if and only if all best linear unbiased…

Gauss–Markov 模型下的实验合并AI 解读

Consider two experiments with homoscedastic models E(Yi ) = Xi θ + Zi ψ, V(Yi ) = σ2 Ini (i = 1, 2). The matrix gi = X'i (Ini — Zi (Z'iZi )Xi can be called the information matrix of linear estimable functions of θ for experiment i. The information matrix g for the combined data (Y 1, Y 2) may be similarly defined. A proof of g ⩾ g 1 + g 2 (⩾ in the sense of nonnegative definiteness) is given, and equality is interpreted. g = g 1 + g 2 if and only if all best linear unbiased…