Box-Cox Transformed D-optimal Design And Composite D-optimal Design

Design of Experiment is an important branch of statistics and what it aims to study are the theories and methodologies for correctly designing experimental programs and analyzing exper-imental data. Optimal Design is an important research branch in Design of Experiment, it is a plan which can meet all the design requirements with a minimum expense. As for Box-Cox Transformation, it is a comprehensive treatment for the data to make it meet the Gauss-Markov condition. The present research is to combine Optimal Design and Box-Cox Transformation together to study D-optimal Design and Compound D-optimal Design after Box-Cox Transfor-mation. For D-optimal Design, the present research will discuss from the following two cas-es:single response and multiple response of linear model and multiple response of non-linear model; the main theoretical basis of it is to infer the approximate decomposition of the expres-sion of information matrix after Box-Cox Transformation by Taylor expansion, and then, in the case of the given parameters of β,σ2,λ, we can determine the D-optimal Design with the help of Fedorov Iteration. For Compound D-optimal Design, a criterion function of Compound D-optimal Design after Box-Cox Transformation is derived from the general criterion function, and it is demonstrated by an example. The present paper is composed of four chapters. In the first chapter, some basic concepts are briefly introduced as well as the background and layout of the present research. The second chapter focuses on the D-optimal Design of linear model and non-linear model after Box-Cox Transformation, and it is demonstrated by a numerical ex-ample. Firstly, we generalize the D-optimal Design under the condition of single response to that under the condition of multiple response; and then find the information matrix M(θ) af-ter Box-Cox Transformation by the definition of Fisher Information Matrix; after that, we will get the appropriate information matrix Ma(θ) with the help of Taylor expansion; finally, the factorization:Ma(θ)=A1A1T+…+AkAkT+Ak+1Ak+1T+…+A2kA2kT will comes into be-ing. In the third chapter, we mainly focus on the Compound D-optimal Design after Box-Cox Transformation. The last chapter of the present paper presents a summary of the present research and at the same time looks to the future research directions.