Admissibility And General Admissibility Of Linear Estimators In Growth Curve Model With Respect To Inequality Restriction

In this thesis,the admissibility and general admissibility of linear estimators in growth curve model with respect to inequality restriction are considered.Some new results are obtained.The thesis is divided into four chapters.In the first chapter,we study the growth curve model:Y=XBZ+ε,(?)～(0,σ²V(?)I),the necessary and sufficient conditions of linear estimates of regression cofficients KBL in the class of homogeneous linear estimators (?)H and nonhomogeneous linear estimators(?)I are gained,under the inequality restriction trNB≥0 and the quadratic loss function tr(d-KBL)(d-KBL)′.In the second chap-ter,we consider the growth curve model of the first chapter with the inequality restriction NB≥0,and give the definition of general admissibility of linear estimates KBL under the matrix loss function(d(Y)-KBL)(d(Y)-KBL)′,the necessary and sufficient con-ditions for general admissible estimates of linear estimates DYF and DYF+C in the class(?)H and(?)I are gained,respectively.In the three chapter,we study the growth curve model:Y_i=XBZ+ε_i,(?)～(0,σ_i² V(?)I),cov((?),(?))= 0,i≠j,i=1,…,m,and obtain the necessary and sufficient conditions for general admissible estimates of linear estimatesΣ_i=1^mD_iY_iF_i andΣ_i=1^mD_iY_iF_i+C in the class of homogeneous linear estimatorsΓH and nonhomogeneous linear estimatorsΓI,under the inequality restriction NB≥0 and the ma-trix loss function(d(Y)-KBL)(d(Y)-KBL)′.In the four chapter,we consider the growth curve model of the three chapter with the inequality restriction trNB≥0,and obtain the necessary and sufficient conditions of KBL in the classΓH andΓI,under the quadratic loss function tr(d-KBL)(d-KBL)′.