二次损失下随机回归系数和参数的所有可容许线性估计

ALL ADMISSIBLE LINEAR ESTIMATORS OF STOCHASTIC REGRESSION COEFFICIENTS AND PARAMETERS

首先列举本文使用的一些记号.设 A 和 B 都是矩阵,A≥0(A>0)表示 A 是非负定(正定)对称阵,A≥B(A>B)表示 A-B≥0(A-B>0);(?)(A)表示 A 的列空间;A^+表示 A 的 Moore-Penrose 广义逆;A^-表示“满足 AA^-A=A”品的 A 的广义逆.

Consider the model Y=Xβ+ε,where β and ε are p-dimensional and n-dime-nsional unobservable random vectors respectively;Y is observable;and X and A are known;∧=V_(22)+XV_(11)X′+XV_(12)+V_(21)X′>0;a∈R^k is a para-meter vector;either σ~2>0 is known or σ~2>0 is also a parameter and rank (XA)<n.The necessary and sufficient condetion for LY+a to be admissible for Sα+Qβwhich is linear estimable under loss(d—Sα—Qβ)′B(d—Sα—Qβ),where B≥0is known,is given.