Combining Experiments Under Gauss-Markov Models
研究了两个同方差实验合并后，信息矩阵与各实验信息矩阵之和的关系，并给出了合并后最佳线性无偏估计等于各实验最佳线性无偏估计线性组合的条件。
Abstract 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 estimators (BLUE's) from the combined experiment are linear combinations of BLUE's from the original experiments. Some characterizations of design matrices are obtained for which the BLUE of p'θ from the combined experiment is a linear combination of the BLUE's of p'θ from the individual experiments, for all p'θ that are estimable in both individual experiments. Key Words: Classical Gauss-Markov modelNuisance parametersInformation matrixEstimable functionsBest linear unbiased estimatorConfounding