Minimax Admissible Estimate Of A Kind Of Multidimension Variable

In this paper,we mainly discuss multivariate liner model and growth curver model, theminimax admissibility of multivariate regression coe?cient for liner estimable function isstudied,some new results were obtained. The thesis is divided into six parts. In the firstpart, we make a brief review about the development in the theory of minimax admissibilityand some matrix introduction relates to this paper. In the second part, we study the multi-variate linear model (Y, XΘ, ), where V > 0 andΣ> 0 are known, under matrix lossfunction, the unique minimax admissible estimate of liner estimable function SΘis givenamong the class of homogeneous (nohomogeneous)linear estimators, see Theorem 2.1 and2.2. In the third part, under another matrix loss function, the unique minimax admissibleestimate of liner estimable function SΘis given among the class of homogeneous linearestimator, see Theorem 3.1. In the fourth part, we study the multivariate liner model withthe equality constraint HΘ= 0, whereΣ≥0 is known, thus under suitable hypotheses,we obtain the unique liner minimax estimate of SΘ, see Theorem 4.1. In the fifth part, westudy the growth curver model( ), where V > 0 andΣ> 0 are known,under quadratic loss function, the unique minimax admissible estimate of linear estimablefunction KBL is given among the homogeneous linear estimator, see Theorem 5.1. In thelast part, we propose some meaningful questions to be solved.