E-optimal designs for polynomial regression without intercept

Journal of Statistical Planning and Inference

Volumn 55, Issue 3, 1996, Pages 371-387

  Chang, Fu Chuen ^b   Heiligers, Berthold ^a  

^a OTTO VON GUERICKE UNIVERSITY   (Germany)

^b NONE

Author keywords

Approximate designs; c optimal designs; Chebyshev approximation; E optimal designs; Equioscillating polynomial; Total positivity; Weak Chebyshev system

Indexed keywords

EID: 0007264924     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-3758(95)00196-4     Document Type: Article

References (18)

1. Atkinson, A.C. and A.N. Donev (1992). Optimum Experimental Designs. Oxford Univ. Press, New York.
2. Cheney, E.W. (1982). Introduction to Approximation Theory. Chelsea, New York.
3. Dette, H. (1993). A note on E-optimal designs for weighted polynomial regression. Ann. Statist. 21, 767-771.
4. Gaffke, N. (1987). Further characterization of design optimality and admissibility for partial parameter estimation in linear regression. Ann. Statist. 15, 942-957.
5. v. Golitschek, M. (1992). Weighted polynomials. In: S.P. Singh, Ed., Approximation Theory, Spline Functions and Applications. Kluwer Academic Publishers, Dordrecht, 139-161.
6. Graybill, F.A. (1983). Introduction to Matrices with Application in Statistic, 2nd ed. Wadsworth, California.
7. Heiligers, B. (1992). E-Optimal Polynomial Regression Designs. Habilitationthesis, Rheinisch Westfälische Technische Hochschule Aachen.
8. Heiligers, B. (1994a). Totally nonnegative moment matrices. Linear Algebra Appl. 199, 213-227.
9. Heiligers, B. (1994b). E-optimal designs in weighted polynomial regression. Ann. Statist. 22, 917-929.
10. Heiligers, B. (1995). Total nonnegativity of moment matrices and its application to E-optimal designs in polynomial regression. In: M. Gasca and C.A. Micchelli, Eds., Total Positivity and its Application. Kluwer Academic Publisher, Dordrecht, forthcoming.
11. Heiligers, B. (1996). Computing E-optimal polynomial regression designs. J. Statist. Plann. Inference, 55, no. 3.
12. Huang, M.-N.L., F.-C. Chang and W.K. Wong (1995). D-optimal designs for polynomial regression without an intercept. Statist. Sinica 5, 441-458.
13. Jones, R.C. and L.A. Karlovitz (1970). Equioscillation and nonuniqueness in the approximation of continuous functions. J. Approx. Theory 3, 138-145.
14. Lau, T.S. (1983). Theory of canonical moments and its applications in polynomial regression. Technical Report No #83-23, Purdue University, USA.
15. Marshall, A.W. and I. Olkin (1979). Inequalities: Theory of Majorization and its Applications. Academic Press, New York.
16. Pukelsheim, F. (1993). Optimal Design of Experiments. Wiley, New York.
17. Pukelsheim, F. and W.J. Studden (1993). E-optimal designs for polynomial regression. Ann. Statist. 21, 402-415.
18. Studden, W.J. (1982). Optimal designs for weighted polynomial regression using canonical moments. In: S.S. Gupta and J.O. Berger, Eds., Statistical Decision Theory and Related Topics III, Vol. 2. Academic Press, New York, 335-350.