D - Optimal Population Design Of Stochastic Coefficient Regression Model Under Heteroscedasticity

This article mainly discusses the heteroscedasticity of simple linear random coefficient regression model D-optimum population designs as well as in this case a quadratic random coefficient regression model D-optimal population design problems.For simple linear random coefficient regression model, we first assume that the random errors are heteroscedasticity. And by calculating, it is concluded that in this case the information matrix. We define the design points on the non-repeat points in time 0,1,2,3,4, and according to the D-optimum design criteria given in the paper, and in this case we obtained the D-optimal design of parameters ? and ?, in order to further study the effect of design points for the optimal design, we have carried out the above time point a simple linear transformation, and we got the linear random coefficient regression model and the corresponding information matrix after the transformation. Then is similar to the second chapter, by calculation, we obtained the D-optimal design after the transformation.In order to better fit, we give a secondary random coefficient regression model in the fourth chapter. For the second random coefficient regression model, we also assume that the random error variance is different. The same points in time 0,1,2,3,4,we can easily see, the D-optimal criterion based on the linear model as well as the quadratic model. By calculation, we obtained the D-optimal design under the hypothesis of the model for the parameter ?. Numerical comparison can be seen in the quadratic model and the linear model, to achieve optimal design points are different.