Minimax robust designs for misspecified regression models

Canadian Journal of Statistics

Volumn 31, Issue 4, 2003, Pages 397-414

  Shi, Peilin ^a   Ye, Jane J ^a   Zhou, Julie ^a  

^a UNIVERSITY OF VICTORIA   (Canada)

Author keywords

Biased regression; Clarke generalized gradient; Least squares; Minimax design; Nonsmooth optimization; Normalizing optimization method; Robust regression design

Indexed keywords

EID: 1642263322     PISSN: 03195724     EISSN: None     Source Type: Journal    
DOI: 10.2307/3315853     Document Type: Article

References (18)

1. G. E. P. Box & N. R. Draper (1959). A basis for the selection of a response surface design. Journal of the American Statistical Association, 54, 622-654.
2. F. H. Clarke (1983). Optimization and Nonsmooth Analysis. Wiley, New York.
3. F. H. Clarke, Yu. S. Ledyaev, R. J. Stern & P. R. Wolenski (1998). Nonsmooth Analysis and Control Theory. Springer, New York.
4. H. Dette & W. K. Wong (1996). Robust optimal extrapolation designs. Biometrika, 83, 667-680.
5. V. V. Fedorov (1972). Theory of Optimal Experiments. Academic Press, New York.
6. G. Heo, B. Schmuland & D. P. Wiens (1999). Restricted minimax robust designs for misspecified regression models. Technical Report 99.04, Statistics Centre, Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada: http://www.stat.ualberta.ca.
7. G. Heo, B. Schmuland & D. P. Wiens (2001). Restricted minimax robust designs for misspecified regression models. The Canadian Journal of Statistics, 29, 117-128.
8. P. J. Huber (1975). Robustness and designs. In A Survey of Statistical Design and Linear Models (J. N. Srivastava, ed.), North-Holland, Amsterdam, pp. 287-303.
9. P. J. Huber (1981). Robust Statistics. Wiley, New York.
10. P. Lancaster & M. Tismenetsky (1985). The Theory of Matrices, Second Edition. Academic Press, New York.
11. K. C. Liu & D. P. Wiens (1997). Robust designs for approximately polynomial regression. Journal of Statistical Planning and Inference, 64, 369-381.
12. J. Sacks & D. Ylvisaker (1984). Some model robust designs in regression. The Annals of Statistics, 12, 1324-1348.
13. P. Shi (2002). Minimax Robust Designs for Misspecified Regression Models. Doctoral dissertation, University of Victoria, Victoria, BC, Canada.
14. S. M. Stigler (1971). Optimal experimental designs for polynomial regression. Journal of the American Statistical Association, 66, 311-318.
15. W. J. Studden (1977). Optimal designs for integrated variance in polynomial regression. In Statistical Decision Theory and Related Topics II: Proceedings of a Symposium held at Purdue University, May 17-19, 1976 (S. S. Gupta & D. S. Moore, eds.), Academic Press, New York, pp. 411-420.
16. D. P. Wiens (1990). Robust minimax designs for multiple linear regression. Linear Algebra and its Applications, 127, 327-340.
17. D. P. Wiens (1992). Minimax designs for approximately linear regression. Journal of Statistical Planning and Inference, 31, 353-371.
18. D. P. Wiens (1993). Designs for approximately linear regressions: maximizing the minimum coverage probability of confidence ellipsoids. The Canadian Journal of Statistics, 21, 59-70.