The Minimax Admissibility Of The Estimable Function And The Linear Prediction Under Quadratic Loss Fuction

In the past decades, the admissibility theory has been studied deeply. In recent years, the minimax admissibility has become more and more popular, which is regarded as a new problem of the admissibility theory.The minimax admissibility of the regression coefficient in the Gauss-Markov model and in the multivariate model under matrix loss has been discussed deeply by some people. Under quadratic loss function, we study the minimax admissibility of the estimate function and the linear prediction.Firstly, we discuss the minimax admissibility of the estimable function of the Gauss-Markov model in class of homogeneous and no homogeneous when the regression coefficient isn't restricted. And by studying the characters of the minimax estimator, we gain the necessary and sufficient conditions of the minimax admissibility of the estimable function of the Gauss-Markov model in class of homogeneous and no homogeneous when the regression coefficient is restricted.Secondly, under quadratic loss function, we study the minimax admissibility of the linear prediction of the Gauss-Markov model with no restriction in the class of homogeneous and gain the necessary and sufficient condition.