Containing Multi-variable Model For Test Design, Controlled Variables And Two Non-parametric Case

In this thesis we mainly study experimental designs for multiresponse models with uncon-trolled variables and the asymptotic Bayesian design for nonparametric multiresponse prediction.The paper is divided into two parts.In the first part, we take the way used in Fedorov and Atkinson (1988) when uncontrolledvariables are included in the multiresponse models. We distinguish among three cases, which areuncontrolled but known variation, uncontrolled and unknown random variation, and uncontrolledbut constant unknown variation respectively. The properties of optimum experimental designsare described in the independent or relative multiresponse model. Moreover, some equivalencetheorems are described under D-optimal and A-optimal criterion.In the second part, we adopt the asymptotics used in Mitchell et al (1994) in nonparametricmultiresponse model. Asymptotic Bayesian design is obtained for nonparametric multirespondeprediction.And it is shown that the uniform continuous design on the unit cube is optimum underthe asymptotic Bayes criterion for a certain prior speci?cation.In Chapter 1, we introduce the relative development in brief. In Chapter 2, we investigateexperimental designs for multiresponse models with uncontrolled variables and prior informationincluding three sections. In Section 1, we study optimal designs for the independent multiresponsewith common controlled and common uncontrolled variables; In Section 2, optimal designs for therelative multiresponse are discussed with common controlled and common uncontrolled variables;In Section 3, there include some different controlled variables in the independent multiresponsemodels based on section 1. In Chapter 3, asymptotic Bayesian design is discussed for nonpara-metric multiresponse prediction.