Robust regression designs for approximate polynomial models |
| |
| Institution: | 1. Department of Mathematics, University of New Orleans, New Orleans, LA 70148, USA;2. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada T6G 2G1;1. School of Energy and Power Engineering, Jiangsu University, Zhenjiang 212013, China;2. Department of Mechanical Engineering, National University of Singapore, Singapore 117576, Singapore;1. KIT, Herman-von-Helmholtz Platz 1, 76344, Eggenstein-Leopoldshafen, Germany;2. Pro-Science GmbH, Parkstrasse 9, Ettlingen, 76275, Germany;1. Department of Mechanical Engineering, University of Antioquia, Medellín, Colombia;2. Department of Chemical Engineering and Biotechnology, University of Cambridge, Philippa Fawcett Drive, Cambridge, CB3 0AS, United Kingdom;3. CARES, Cambridge Centre for Advanced Research and Education in Singapore, 1 Create Way CREATE Tower, 05-05, Singapore, 138602;4. State Key Lab of Explosion Science and Technology, Beijing Institute of Technology, Beijing, 100081, China;5. School of Chemical and Biomedical Engineering, Nanyang Technological University, 62 Nanyang Drive, Singapore, 63745 |
| |
| Abstract: | In this article, we consider robust designs for approximate polynomial regression models, by applying the theory of canonical moments. The design criterion, first given in Liu and Wiens (J. Statist. Planning Inference 64 (1997) 369), is to maximize the determinant of the information matrix subject to a side condition of bounding the bias arising from model misspecification. We give a new proof of, and extend, the main theorem in Liu and Wiens (op. cit.); in so doing we shed new light on the structure of this problem. New designs, with the further property of minimizing the generalized variance of the additional regression coefficients when an enlarged model is fitted, are derived and assessed. These provide additional robustness against uncertainty regarding the proper degree of the fitted polynomial response. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
