Restricted minimax robust designs for misspecified regression models

Canadian Journal of Statistics

Volumn 29, Issue 1, 2001, Pages 117-128

  Heo, Giseon ^a   Schmuland, Byron ^a   Wiens, Douglas P ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Biased regression; Least squares; Optimal design; Ozonation; Polynomial regression; Second order design

Indexed keywords

EID: 0035628923     PISSN: 03195724     EISSN: None     Source Type: Journal    
DOI: 10.2307/3316055     Document Type: Article

References (19)

1. D. A. Andrews & A. M. Herzberg (1979). The robustness and optimality of response surface designs. Journal of Statistical Planning and Inference, 3, 249-257.
2. 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.
3. H. Dette & W. K. Wong (1996). Robust optimal extrapolation designs. Biometrika, 83, 667-680.
4. V. V. Fedorov (1972). Theory of Optimal Experiments. Academic Press, New York.
5. G. Heo (1998). Optimal Designs for Approximately Polynomial Regression Models. Unpublished doctoral dissertation, University of Alberta, Edmonton, Alberta, Canada.
6. G. Heo & W. James (1995). The Effects of Ozone Application Rate and Gas: Liquid Ratio on Removing Fine Suspended Particles in a Bubble Column Reactor. Technical report, Alberta Environmental Centre.
7. 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.
8. P. J. Huber (1975). Robustness and designs. In A Survey of Statistical Design and Linear Models: Proceedings of an International Symposium on Statistical Design and Linear Models, Colorado State University, Fort Collins, March 19-23, 1973 (J. N. Srivastava, ed.), North Holland, Amsterdam, pp. 287-303.
9. P. J. Huber (1981). Robust Statistics. Wiley, New York.
10. K. C. Li & W. Notz (1982). Robust designs for nearly linear regression. Journal of Statistical Planning and Inference, 6, 135-151.
11. S. X. Liu & D. P. Wiens (1997). Robust designs for approximately polynomial regression. Journal of Statistical Planning and Inference, 64, 369-381.
12. k. The Annals of Statistics, 10, 511-525.
13. J. Sacks & D. Ylvisaker (1984). Some model robust designs in regression. The Annals of Statistics, 12, 1324-1348.
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. Statistical Decision Theory and Related Topics II: Proceedings of a Symposium, Purdue University, Lafayette, Indiana, 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, Second Special Issue on Linear Algebra and Statistics, 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 (1998). Minimax robust designs and weights for approximately specified regression models with heteroscedastic errors. Journal of the American Statistical Association, 93, 1440-1450.
19. D. P. Wiens (2000). Robust weights and designs for biased regression models: Least squares and generalized M-estimation. Journal of Statistical Planning and Inference, to appear.