Optimal Designs For Varying Coefficient Mixture Experiment

At present, the studies of experiment designs are based on the linear model-s,however we all know that the data which has been given from the industry,agricultureand science test is more and more complex,because that people play more and moreattention to the research of nonlinear models which is in a new area.The varying co-efficient regression mixture models is a typical nonlinear models that this thesis con-cerned with.In our research,we attempt this model to mixed effects models.The thesis concludes five chapters.In the first chapter,we describe the basic background,the purpose,the signifi-cance and the contents of the research.In the second chapter,we introduce the experiment designs which include theoptimal designs and the mixture in detail,mainly analysis of D optimal designs,G optimal designs,A optimal designs,I optimal designs,and the simplex-centroid de-signs.Chapter3,we analyze the definition of mixed effects models,and then we givethe parameters estimate for fixed effects and varying effects.Chapter4,we structure and analyze the varying coefficient2-component mix-ture regression models,then,we give its D optimal designs,G optimal designs,A optimal designs,I optimal designs.In the final chapter,we give the varying coefficient3-component mixture regres-sion models,then,we give its A optimal designs,I optimal designs.At the last,wegive the summary and the direction of the research in the future.