摘要
This paper considers the simultaneous estimation of linear function tr(D’B)+tr(C∑) of the regression coefficients matrix B and the covariance matrix ∑,and gives(i) the MINQLE(U,I) tr(D’B)+tr(C∑) of an estimable function tr(O’B)+tr(C∑); (ii) the n.s.conditions for tr(D’B)+tr(C∑) to be the UMVIQLUE of tr(D’B)+tr(C∑);(iii) the n.s.conditions for tr(D’B)+tr(C∑)’s UMVIQLUE to be existent,and shows that tr(D’B) +tr(C∑) is just the UMVIQLUE of tr(D’B)+tr(C∑) (provided a UMVIQLUE exists);(iv) the n.s.conditions for any invariant quadratic plus linear estimation y’MAMy + a’y to be the UMVIQLUE of tr(D’B)+tr(C∑).
This paper considers the simultaneous estimation of linear function tr(D'B)+tr(C∑) of the regression coefficients matrix B and the covariance matrix ∑,and gives(i) the MINQLE(U,I) tr(D'B)+tr(C∑) of an estimable function tr(O'B)+tr(C∑); (ii) the n.s.conditions for tr(D'B)+tr(C∑) to be the UMVIQLUE of tr(D'B)+tr(C∑);(iii) the n.s.conditions for tr(D'B)+tr(C∑)'s UMVIQLUE to be existent,and shows that tr(D'B) +tr(C∑) is just the UMVIQLUE of tr(D'B)+tr(C∑) (provided a UMVIQLUE exists);(iv) the n.s.conditions for any invariant quadratic plus linear estimation y'MAMy + a'y to be the UMVIQLUE of tr(D'B)+tr(C∑).
基金
Project supported by the National Natural Science Foundation of China
