Robust Designs for Approximately Linear Regression Models With Correlated Errors

摘要

经典最优设计理论假定响应曲面为真,不同试验点之间相互独立.但实际情况比较复杂,响应曲面可能存在偏差,试验观察值之间也可能存在相依性.因此经典理论得到的设计就存在一定的风险性.为降低设计风险,本文从一般模型出发研究模型的稳健试验设计问题.着重考虑了不同偏差函数和误差结构下获得最优设计的设计准则,并通过实例考察了不同设计准则下设计的稳健性.

目录

文摘

英文文摘

关于学位论文使用授权的说明

Chapter 1 Introduction

Chapter 2 Robust Designs for Models With MA(q) Errors

2.1 Preliminaries

2.2 Design criteria for models with correlated errors

2.3 Case study

2.4 Conclusion and Discussion

Chapter 3 Robust Designs for Models With known Correlated Errors

3.1 Formulation for the design problem

3.2 Illustrative Example

3.3 Summary

Chapter 4 Bayesian Robust Design

4.1 Formulation of the Bayesian Design Criteria

4.2 Algorithm

4.3 Numerical Results and Discussion

4.3.1 Bayesian designs for models with MA(1) errors

4.3.2 Bayesian designs for models with MA(2) errors

4.4 Summery

Bibliography

Appendix A Proof of Theorem 2.1 and Theorem 2.2

Appendix B Proof of Theorem 2.3

致谢

声明

在学期间完成论文情况