Nonlinear Mixture Model And It’s Optimal Design

An efficient method of learning about the world is well-designed experi-ment,since the random error cannot be avoid easily,it is very essential to choose suit-able statistical methods for higher efficient design and analysis.For the problems of optimal design in nonlinear mixture model,the fisher infor-mation matrix depends on certain nuisance parameters which are unknown and whichenter the model nonlinearly.A new strategy to deal with this problem is to use theFunctional approach,that give a new method to construct the fisher information ma-trix,then we can use the criterion to construct a real-valued function with it.In thepresent paper we explore the mixture models for which the associated criteria aredifferentiable.In the first chapter,the basic concepts and results of optimal design theory arebriefly described,also here give some basic background about experimental designand mixture experimental design,there also some fundamental idea on the analysis ofnonlinear mixture model’s optimal design and it’s background.Then in the end of thischapter the main work of this paper will be introduced.In the second chapter,the basic of mixture design will be introduced,the widelyused iterative numerical techniques for finding optimal design will be provide.Theimplicit functional theorem and basic properties of chebyshev systems providing im-portant tools for the functional approach.Chapter3,this chapter will develop a general theory for the functional ap-proach.Also it will devote to studying locally D-optimal efficient design for nonlin-ear regression models of a Chebyshev type.It can be proved that some times,supportpoints of the optimal designs are monotonic functions of initial values of nonlinearparameters.The last chapter,D-optimal designs is constructed for rational mixture model,alsoa method of construct E-optimal design will be introduced.