多元线性模型中回归系数矩阵的Minimax估计

Minimax estimator for multivariate linear model of regression coefficient matrix

考虑多元线性模型Y=XΘ+ε,E(ε)=0,COV(ε)=σ2ΔΣ,其中Δ>0,而Σ≥0是已知矩阵,考虑了其回归系数矩阵的Minimax估计问题,在矩阵损失下,讨论了线性估计的性质,并在适当假设下,得到了系数矩阵的线性可估函数SΘ的惟一Minimax估计。

For the multivariate linear model Y=XΘ＋ε,E（ε）=0,COV（ε）=σ^2ΔΣ,where Δ〉0,and Σ≥0 are known matrix, the minimax estimator of regression coefficients matrix in the multivariate linear model was considered. Under the matrix loss function, the property of linear estimators was investigated. The unique minimax estimator of linearly estimable functions SΘ of coefficients matrix was obtained under the suitable hypotheses.