Minimax Estimation Of Correlation Coefficient Of Two Models Under The Quadratic Loss

In this paper,we mainly study the Minimax estimation of correlation coefficient of two models under the quadratic loss.Firstly,this paper introduces briefly some basic theoretical knowledge and the definition of loss function in the linear model.Some basic concepts of statistical decision function and the definition of Minimax estimation are also introduced.Secondly,under the quadratic loss,using Minimax estimation in statistical decision theory,The Minimax estimation of random regression coefficient b and parameter vertora In the random effect model and the maximum risk is studied.The properties of linear Minimax estimators of the linear of functions Sα+Qβ composed by a and b is discussed,and then conclusion is that the estimated function Sα+Qβexists Minimax estimation in the class of general estimation,Sα+Qβ and it gives the specific expression of the maximum risk,but also under special conditions,it is unique.Finally,with the method of Minimax estimation of regression coefficient of linear model under the quadratic loss.The Minimax of general nonlinear model coefficients is studied by using the stochastic optimization theory to establish the relation between Minimax estimation of nonlinear model coefficient and stochastic optimization.So,it can solve the problem of general nonlinear Minimax model coefficient estimated by stochastic optimization theory.