Optimal designs for the identification of the order of a Fourier regression

Annals of Statistics

Volumn 26, Issue 4, 1998, Pages 1496-1521

  Dette, Holger ^a   Haller, Gerd ^a  

^a RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

Canonical moments; Fourier regression model; Heteroscedastic polynomial regression; Model discrimination; Optimal design

Indexed keywords

EID: 0032336338     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1024691251     Document Type: Article

References (31)

1. ABRAMOWITZ, M. and STEGUN, I. A. (1964). Handbook of Mathematical Functions. Dover, New York.
2. ANDERSON, T. W. (1962). The choice of the degree of a polynomial regression as a multiple decision problem. Ann. Math. Statist. 33 255-265.
3. ANDERSON, T. W. (1994). The Statistical Analysis of Time Series. Wiley, New York.
4. ATKINSON, A. C. (1972). Planning experiments to detect inadequate regression models. Biometrika 59 275-293.
5. ATKINSON, A. C. and Cox, D. R. (1974). Planning experiments for discriminating between models (with discussion). J. Roy. Statist. Soc. Ser. B 36 321-348.
6. ATKINSON, A. C. and DONEV, A. N. (1992). Optimum Experimental Designs. Oxford Univ. Press.
7. DETTE, H. (1994). Discrimination designs for polynomial regression on a compact interval. Ann. Statist. 22 890-904.
8. DETTE, H. (1995). Optimal designs for identifying the degree of a polynomial regression. Ann. Statist. 23 1248-1267.
9. DETTE, H. and STUDDEN, W. J. (1997). The Theory of Canonical Moments with Applications in Statistics, Probability and Analysis. Wiley, New York.
10. FEDOROV, V. V. (1972). Theory of Optimal Experiments. Academic Press, New York.
11. HILL, P. D. H. (1978). A note on the equivalence of D-optimal design measures for three rival linear models. Biometrika 65 666-667.
12. HOEL, P. G. (1965). Minimax designs in two-dimensional regression. Ann. Math. Statist. 36 1097-1106.
13. KARLIN, S. and STUDDEN, W. J. (1966). Tchebycheff Systems: With Applications in Analysis and Statistics. Interscience, New York.
14. KIEFER, J. C. (1974). General equivalence theory for optimum designs. Ann. Statist. 2 849-879.
15. LAU, T. S. (1983). Theory of canonical moments and its applications in polynomial regression I, II. Technical Reports 83-23, 83-24, Purdue Univ.
16. LAU, T. S. (1988). D-optimal designs on the unit q-ball. J. Statist. Plann. Inference 19 299-315.
17. LAU, T. S. and STUDDEN, W. J. (1985). Optimal designs for trigonometric and polynomial regression. Ann. Statist. 13 383-394.
18. MARDIA, K. (1972). The Statistics of Directional Data. Academic Press, New York.
19. PUKELSHEIM, F. (1993). Optimal Design of Experiments. Wiley, New York.
20. RICCOMAGNO, E., SCHWABE, R., and WYNN, H. P. (1997). Lattice-based D-optimum design for Fourier regression. Ann. Statist. 25 2313-2327
21. RIVLIN, T. J. (1990). Chebyshev Polynomials. Wiley, New York.
22. SKIBINSKY, M. (1967). The range of the (n + 1)th moment for distributions on [0, 1]. J. Appl. Probab. 4 543-552.
23. SKIBINSKY, M. (1969). Some striking properties of binomial and beta moments. Ann. Math. Stast. 40 1753-1764.
24. SKIBINSKY, M. (1986). Principal representations and canonical moment sequences for distributions on an interval. J Math. Anal. Appl. 120 95-120.
25. SPRUILL, M. G. (1990). Good designs for testing the degree of a polynomial mean. Sankhyā Ser. B 52 67-74.
26. STUDDEN, W. J. (1968). Optimal designs on Chebshev points. Ann. Math. Statist. 39 1435-1447.
27. s-optimal designs for polynomial regression using continued fractions. Ann. Statist. 8 1132-1141.
28. STUDDEN, W. J. (1982a). Some robust-type D-optimal designs in polynomial regression. J. Amer. Statist. Assoc. 77 916-921.
29. STUDDEN, W. J. (1982b). Optimal designs for weighted polynomial regression using canonical moments. In Statistical Decision Theory and Related Topics 3 (S. S. Gupta and J. O. Berger, eds.) 335-350. Academic, New York.
30. p-optimal design for polynomial regression. Ann. Statist. 17 618-623.
31. VAN ASSCHE, W. (1987). Asymptotics for Orthogonal Polynomials. Lecture Notes in Math. 1265. Springer, New York.