Constructing c-optimal designs for polynomial regression with no intercept
DOI:
https://doi.org/10.21638/11701/spbu01.2020.215Abstract
-
Keywords:
c-optimal designs, f'(z)-optimal designs, optimal designs for estimating the slope, polynomial regression models with no intercept
Downloads
Download data is not yet available.
References
1. Pukelsheim F., Studden W. J. E-optimal designs for polynomial regression // Annals of Statistics. 1993. Vol. 21, no. 1. P. 402-415.
2. Fedorov V. V., Hackl P. Model-Oriented Design of Experiments. New York: Springer, 1997.
3. Atkinson A. C., Donev A. N., Tobias R. D. Optimum Experimental Designs, with SAS. Oxford: Oxford University Press, 2007.
4. Hoel P. G. Efficiency problems in polynomial estimation // Annals of Mathematical Statistics. 1958. Vol. 29, no. 4. P. 1134-1145.
5. Studden W. J. Ds -Optimal Designs for Polynomial Regression Using Continued Fractions // Annals of Statistics. 1980. Vol. 8, no. 5. P. 1132-1141.
6. Dette H. A generalization of D- and D1-optimal designs in polynomial regression // Annals of Statistics. 1990. Vol. 18. P. 1784-1805.
7. Dette H., Franke T. Robust designs for polynomial regression by maximizing a minimum of D- and D1-efficiencies // Annals of Statistics. 2001. Vol. 29, no. 4. P. 1024-1049.
8. Zen M.-M., Tsai M.-H. C riterion-robust optimal designs for model discrimination and parameter estimation in Fourier regression models // Journal of Statistical Planning and Inference. 2004. Vol. 124. P. 475-487.
9. Dette H. A Note on E-Optimal Designs for Weighted Polynomial Regression // Annals of Statistics. 1993. Vol. 21, no. 2. P. 767-771.
10. Heiligers B. E-Optimal Designs in Weighted Polynomial Regression // Annals of Statistics. 1994. Vol. 22, no. 2. P. 917-929.
11. Dette H., Studden W. J. Geometry of E-optimality // Annals of Statistics. 1993. Vol. 21, no. 1. P. 416-433.
12. Studden W. J. Optimal designs on Tchebycheff points // Annals of Mathematical Statistics. 1968. Vol. 39, no. 5. P. 1435-1447.
13. Elfving G. Optimal allocation in linear regression theory // The Annals of Mathematical Statistics. 1952. Vol. 23. P. 255-262.
14. Atkinson A. C. The Design of Experiments to Estimate the Slope of a Response Surface // Biometrika. 1970. Vol. 57, no. 2. P. 319-328.
15. Murthy V., Studden W. Optimal designs for estimating the slope of a polynomial regression // J. Am. Statist. Assoc. 1972. Vol. 67. P. 869-873.
16. Myres R., Lahoda S. A generalization of the response surface mean square error criterion with a specific application to the slope // Technometrics. 1975. Vol. 17. P. 481-486.
17. Ott L., Mendenhall W. Designs for Estimating the Slope of a Second Order Linear Model // Technometrics. 1972. Vol. 14. P. 341-353.
18. Hader R., Park S. Slope-rotatable central composite designs // Technometrics. 1978. Vol. 20. P. 413-417.
19. Mandal N., Heiligers B. Minimax designs for estimating the optimum point in a quadratic response surface // Journal of Statistical Planning and Inference. 1992. Vol. 31. P. 235-244.
20. Pronzato L., Walter E. Experimental design for estimating the optimum point in a response surface // Acta Applicandae Mathematicae. 1993. Vol. 33. P. 45-68.
21. Melas V., Pepelyshev A., Cheng R. Designs for estimating an extremal point of quadratic regression models in a hyperball // Metrika. 2003. Vol. 58. P. 193-208.
22. Dette H., Melas V. B., Pepelyshev A. Optimal designs for estimating the slope of a regression // Statistics. 2010. Vol. 44, no. 6. P. 617-628.
23. Dette H., Melas V. B., Shpilev P. Some explicit solutions of c-optimal design problems for polynomial regression with no intercept // Annals of the Institute of Statistical Mathematics. 2020. DOI: 10.1007/s10463-019-00736-0
24. Pukelsheim F. Optimal Design of Experiments. Philadelphia: SIAM, 2006.
25. Kiefer J. General Equivalence Theory for Optimum Designs (Approximate Theory) // The Annals of Statistics. 1974. Vol. 2, no. 5. P. 849-879.
26. Dette H., Melas V. B., Pepelyshev A. Optimal designs for estimating individual coefficients in polynomial regression - a functional approach // Journal of Statistical Planning and Inference. 2004. Vol. 118, no. 1. P. 201-219.
27. Wynn H. P. The sequential generation of D-optimal experimental designs // Annals of Mathematical Statistics. 1970. Vol. 41, no. 5. P. 1655-1664.
28. Melas V. B. Functional approach to experimental optimal design. Heidelber: Springer, 2006.
Downloads
Published
2020-08-15
How to Cite
Melas, V. B., & Shpilev, P. V. (2020). Constructing c-optimal designs for polynomial regression with no intercept. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 7(2), 331–342. https://doi.org/10.21638/11701/spbu01.2020.215
Issue
Section
Mathematics
License
Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.