D-optimal Designs In Random Coefficient Regression Models

This paper studies the efficiency of the D—optimal design in the original heteroskedascicjty model in the case of random intercept heterOscedasticjty model and random slope model;prob—lems of D—optimal design in the two different heterOscedasticity structures;attempt to derive the equivalence theorem in more general error structure;and the D—optimal design for the first order random coefficient regression model in the circular domain.For the efficiency of the D—optimal design in the original heteroskedasticity model in the case of random intercept hecerOscedasticitv model and random slope model We first give the definition ofD^一efficiency;then give the Dλ一efficiency in the case of random intercept heterOscedasticity model and random slope model,and make the assumption that the random coel'ficient regression hcterosce(1asticity model has the homogeneity of variance.For the problems of D—optimal design in the two different hcteroscedasticitv structures in the case of random intercept model random slope model.This paper construct D—optimal design in the two different hetel'oscedasticity structnres,in addition,try to give equivalence theorem in the more genet'al heterOscedasticity structuresFor the first orde r'Randonl Coefficient Regression Model in the oilcular domains,By the Loewner order,we proved that D-optimal design Call be acquired in the four ertices of a square with certain conditions Then,we give D-optimal design in the model of closed circle.