Response Model Discrimination,

Atkinson and Fedorov proposed T-optimal criterion in order to deal with the optimal design of discriminating between several rival models.After that,we realize the theoretical and practical significance and they also showed us somewhat about the discrimination between rival models.Many people studied the issue about different kinds of models,such as Burke et al(1994), Ponce de leonand Atkinson(1991),Milller å'Œ Ponce de lean(1996),and so on.But,the critenons that they proposed all concerned only on single response models.Based on the theory about single response models,what we mainly discuss here is how to find the optimal design of discriminating between multiresponse models.In Chapter 2,we introduced some theory about the discrimination between single response models.We consider instead design when a choice is to be made between two or more competing models neither of which is ,in general ,a special case of the other.(If not ,we could set a constraint on the parameter values in order to make two models separated)According to what Atkinson &Fedorov(1975a,b)have proposed,we mainly consider the residual sum of squares between the models ,and what we try to do is to find a design to make the residual sum of squares arrives maximum.If there are two or more models,as our purpose is try to discriminate the given models,what we should do is only to find a design which ensures that it could make the residual sum of squares between the closest models arrives maximum.So,what we should first do is to compute the residual sum of squares among the models.If there is only one model that is closest to the true model,we could find a design that makes the residual sum of squares between the two models arrive maximum;If there are two or more closest models ,they require different weights in the design criterion.Thus we could find a design that makes the new criterion arrive maximum.In Chapter 3,we try to find the optimal design for for discrimination between two multiresponse models.Due to the fact that single response model is different from multiresponse model and the response is not a number ,but a vector,we should first set the response vector which is formed by response parameters before we consider the criterion.Another problem that we should not ignore is correlation of the response parameters in one multiresponse model,so we should add it to our criterion while we set the criterion and estimate the parameters.Thus,we introduced the Euclidean norm to duel with the problem.In subsection I,we duel with the problem that how to set the T-opt design when the two multiresponse models are standard normal correlation.After that ,we also give the necessary and sufficient condition of the T-opt design.In subsection 2,we discussed the problem that how to set the T-opt design when the two multiresponse models are generally normal correlation.As we all know,the covariance matrix is symmetric and positive defi-...