E-optimal designs for polynomial spline regression

Journal of Statistical Planning and Inference

Volumn 75, Issue 1, 1998, Pages 159-172

  Heiligers, Berthold ^a  

^a Universitat   (Germany)

Author keywords

62K05* B basis* B splines; Chebyshev spline; E optimal design; Equi oscillation; Oscillation matrix; Remez exchange algorithm; Scalar optimal design; Total positivity; Truncated powers

Indexed keywords

EID: 0007329968     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0378-3758(98)00133-5     Document Type: Article

References (29)

1. Ando T. Totally positive matrices. Linear Algebra Appl. 90:1987;165-219.
2. Bellman, R., 1960. Introduction to Matrix Analysis. McGraw-Hill, New York.
3. deBoor C., Pinkus A. The approximation of a totally positive band matrix by a strictly positive one. Linear Algebra Appl. 42:1982;81-98.
4. Carnicer J.M., Peña J.M. Totally positive bases for shape preserving curve design and optimality of B-splines. Comput. Aided Geom. Des. 11:1994;633-654.
5. Cheney, E.W., 1982. Introduction to Approximation Theory, 2nd ed. Chelsea, New York.
6. Dette H. Designing experiments with respect to 'standardized' optimality criteria. J. Roy. Statist. Soc. B. 59:1997;97-110.
7. Gaffke, N., 1982. Optimalitätskriterien und optimale Versuchspläne. Habilitationthesis, Rheinisch-Westfälische Technische Hochschule Aachen, Germany (in German).
8. Gaffke N. Further characterizations of design optimality and admissibility for partial parameter estimation in linear regression. Ann. Statist. 15:1987;942-957.
9. Gaffke, N., Heiligers, B., 1998. Optimal approximate designs for B-spline regression with multiple knots. To appear in: Park, S.H., Vining, G.G. (Eds.), Statistical Process Monitoring and Optimization. Marcel Dekker, New York.
10. Heiligers, B., 1992. E-optimal polynomial regression designs. Habilitationthesis, Rheinisch-Westfälische Technische Hochschule Aachen, Germany.
11. Heiligers B. E-optimal designs in weighted polynomial regression. Ann. Statist. 22:1994;917-929.
12. Heiligers B. Totally nonnegative moment matrices. Linear Algebra Appl. 199:1994;213-227.
13. Heiligers B. Computing E-optimal polynomial regression designs. J. Statist. Plann. Inference. 55:1996;219-233.
14. Kaishev V.K. Optimal experimental design for B-spline regression. Comput. Statist. Data Anal. 8:1989;39-47.
15. Karlin, S., 1968. Total Positivity, vol. I. Stanford Univ. Press, Stanford, CA.
16. Kiefer J.C. On the nonrandomized optimality and randomized nonoptimality of symmetrical designs. Ann. Math. Statist. 29:1958;675-699.
17. Kiefer, J.C., 1975. Construction and optimality of generalized Youden designs. In: Srivastava, J.N. (Ed.), A Survey of Statistical Design and Linear Models. North-Holland, Amsterdam, pp. 333-353.
18. Lim Y.B. D-optimal design in polynomial spline regression. Korean J. Appl. Statist. 4:1991;171-178.
19. Mørken, K., 1996. Total positivity and splines. In: Gasca, M., Micchelli, C.M. (Eds.), Total Positivity and Its Applications. Kluwer Academic Press, Dordrecht, pp. 47-84.
20. Murty V.N. Optimal designs with a Tchebycheffian spline regression function. Ann. Math. Statist. 42:1971;643-649.
21. Murty V.N. Optimal designs with a polynomial spline regression with a single multiple knot at the center. Ann. Math. Statist. 42:1971;952-960.
22. Park S.H. Experimental designs for fitting segmented polynomial regression models. Techometrics. 20:1978;151-154.
23. Pinkus, A., 1996. Spectral properties of totally positive kernels and matrices. In: Gasca, M., Micchelli, C.M. (Eds.), Total Positivity and Its Applications. Kluwer Academic Press, Dordrecht, pp. 477-511.
24. Pukelsheim, F., 1993. Optimal Design of Experiments. Wiley, New York.
25. Pukelsheim F., Studden W.J. E-optimal designs for polynomial regression. Ann. Statist. 21:1993;402-415.
26. Studden W.J. Optimal designs on Tchebycheff points. Ann. Math. Statist. 39:1968;1435-1447.
27. Studden, W.J., 1971. Optimal design and spline regression. In: Rustagi, J.S. (Ed.), Optimizing Methods in Statistics. Academic Press, New York, pp. 63-76.
28. Studden W.J., VanArman D.J. Admissible designs for polynomial spline regression. Ann. Math. Statist. 40:1969;1557-1569.
29. Watson, G.A., 1980. Approximation Theory and Numerical Methods. Wiley, New York.