Robust designs based on the infinitesimal approach

Journal of the American Statistical Association

Volumn 92, Issue 440, 1997, Pages 1503-1511

  Wiens, Douglas P ^a   Zhou, Julie ^b  

^a UNIVERSITY OF ALBERTA   (Canada)

^b LAKEHEAD UNIVERSITY   (Canada)

Author keywords

Approximately linear regression response; B robustness; M robustness; Regression design; V robustness

Indexed keywords

EID: 0031315370     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1997.10473672     Document Type: Article

References (30)

1. Bickel, P. J., and Herzberg, A M.(1979), "Robustness of Design Against Autocorrelation in Time I: Asymptotic Theory, Optimality for Location and Linear Regression,"The Annals of Statistics, 7, 77-95.
2. Bischoff, W.(1992), "On Exact D-Optimal Designs for Regression Models With Correlated Observations,"Annals of the Institute of Statistical Mathematics, 44, 229-238.
3. Bischoff, W. (1993), "On D-Optimal Designs for Linear Models Under Correlated Observations With an Application to a Linear Model With Multiple Response,"Journal of Statistical Planning and Inference, 37, 69-80.
4. Box, G. E. P., and Draper, N. R.(1959), "A Basis for the Selection of a Response Surface Design,"Journal of the American Statistical Association, 54,622-654.
5. Constantine, G. M.(1989), "Robust Designs for Serially Correlated Observations,"Biometrika, 76, 245-251.
6. Field, C. A, and Wiens, D. P.(1994), "One-Step M Estimators in the Linear Model, With Dependent Errors,"Canadian Journal of Statistics,22,219-231.
7. Grenander, U., and Szego, G.(1958), Toeplitz Forms and Their Application, Berkeley: University of California Press.
8. Hampel, F. R., Ronchetti, E., Rousseeuw, R. J., and Stahel, W.(1986), Robust Statistics: The Approach Based on Influence Functions, Toronto: Wiley.
9. Herzberg, A M., and Huda, S.(1981), "A Comparison of Equally Spaced Designs With Different Correlation Structures in One and More Dimensions,"Canadian Journal of Statistics, 9, 203-208.
10. Hossjer, O.(1991), "The Change-of-Variance Function for Dependent Data,"Probability Theory and Related Fields, 90, 447-467.
11. Huber, P. J.(1975), "Robustness and Designs," in A Survey of Statistical Design and Linear Models, ed. J. N. Srivastava, Amsterdam: NorthHolland, pp. 287-303.
12. Jenkins, G. M., and Chanmugam, J.(1962), "The Estimation of Slope When the Errors are Autocorrelated,"Journal of the Royal Statistical Society, Ser. B, 24, 199-214.
13. Judickii, M. I.(1976), "On Designing Experiments to Estimate the Parameters in Regression Models With Correlated Errors in the Observations,"Theory of Probability and Mathematical Statistics, 11, 173-180.
14. Kiefer, J., and Wynn, H. P.(1984), "Optimum and Minimax Exact Treatment Designs for One-Dimensional Autoregressive Error Process,"The Annals of Statistics, 12, 414-450.
15. Li, K. c., and Notz, W.(1982), "Robust Designs for Nearly Linear Regression,"Journal of Statistical Planning and Inference, 6, 135-151.
16. Liu, S. X.(1994), "Some Topics in Robust Estimation and Experimental Design," unpublished Ph.D. dissertation, University of Calgary, Dept. of Mathematics and Statistics.
17. Liu, S. X., and Wiens, D. P. (in press), "Robust Designs for Approximately Polynomial Regression," Journal of Statistical Planning and Inference, 64.
18. Pesotchinsky, L. (1982), "Optimal Robust Designs: Linear Regression in Rk," The Annals of Statistics, 10,511-525.
19. Pukelsheim, F.(1993), Optimal Design of Experiments, Toronto: Wiley.
20. Sacks, J., and Ylvisaker, D.(1966), "Designs for Regression Problems With Correlated Errors,"The Annals of Statistics, 37, 66-89.
21. Sacks, J., and Ylvisaker, D. (1968), "Designs for Regression Problems with Correlated Errors; Many Parameters," The Annals of Statistics, 39, 49-69.
22. Sacks, J., and Ylvisaker, D. (1970), "Designs for Regression Problems With Correlated Errors, III,"The Annals of Statistics, 41, 2057-2074.
23. Samarov, A M.(1987), "Robust Spectral Regression,"The Annals of Statistics, 15,99-111.
24. Srivastava, M. S., and Khatri, C. G.(1979), An Introduction to Multivariate Statistics, New York: North-Holland.
25. Tang, D.(1993), "Minimax Regression Designs Under Uniform Departure Models,"The Annals of Statistics, 21, 434-446.
26. Werther, J., Hartge, E.-U., and Rensner, D.(1990), "Messtechniken Fuer Gas/Feststoff-Wirbelschichtreaktoren,"Chemie-Ingenieur- Tecknik, 62, 605-613.
27. Wiens, D. P.(1991), "Designs for Approximately Linear Regression: Two Optimality Properties of Uniform Designs,"Statistics and Probability Letters, 12, 217-221.
28. Wiens, D. P. (1992), "Minimax Designs for Approximately Linear Regression,"Journal of Statistical Planning and Inference, 31, 353-371.
29. Wiens, D. P., and Zhou, J.(1995), "Minimax Designs for Approximately Linear Models With AR(1) Errors," Technical Report 95.01, University of Alberta, Statistics Centre, Dept. of Mathematical Sciences.
30. Wiens, D. P., and Zhou, J. (1996), "Minimax Regression Designs for Approximately Linear Models With Autocorrelated Errors,"Journal of Statistical Planning and Inference, 55, 95-106.