矩阵损失下随机回归系数和参数的线性Minimax估计(英文)

THE LINEAR MINIMAX ESTIMATOR OF STOCHASTIC REGRESSION COEFFICIENTS AND PARAMETERS UNDER MATRIX LOSS FUNCTION

对于一般的随机效应线性模型 Y=Xβ+ ε,这里 β和 ε分别是 p维和 n维的随机向量 ,且E βε =Aa0 , Cov βε =σ2 V100 V2,(Vi ≥ 0 ,i =1,2 )我们定义了 Sα+ Qβ的线性 Minimax估计 ,在一定条件下得到了 Sα+ Qβ在线性估计类中的 Minimax估计 ,并在几乎处处意义下证明了它的唯一性 .

For the general stochastic effects linear model Y=Xβ+ε where β and ε are p dimensional and n dimensional unobservable random vectors respectively with Eβ ε=Αα 0 and Covβ ε=σ 2V 10 0V 2 (V i≥0,i=1,2) , we define the linear minimax estimator of Sα+Qβ. Under some restrictions, the minimax estimator of Sα+Qβ in the class of linear estimators, which is unique with probability 1, is obtained.