Abstract
In his book Pukelsheim [8] pointed out that designs supported at the arcsin points are very efficient for the statistical inference in a polynomial regression model. In this note we determine the canonical moments of a class of distributions which have nearly equal weights at the arcsin points. The class contains theD-optimal arcsin support design and theD 1-optimal design for a polynomial regression. The results allow explicit representations ofD-, andD 1-efficiencies of these designs in all polynomial models with a degree less than the number of support points of the design.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Anderson TW (1962) The choice of the degree in a polynomial regression as a multiple decision problem. Ann. Math. Statist. 33:255–265
Chihara TS (1978) Introduction to orthogonal polynomials. Gordon and Breach, New York
Dette H (1994) Discrimination designs for polynomial regression on compact intervals. Ann. Statist. 22:890–903
Dette H, Studden WJ (1997) The theory of canonical moments with applications in statistics, probability and analysis. Wiley, New York
Karlin, Studden WJ (1966) Tchebycheff systems: With applications in analysis and statistics. Interscience Publishers, Wiley, New York
Kiefer J (1974) General equivalance theory for optimum designs (approximate theory). Ann. Statist. 2:849–879
Läuter E (1974) Experimental design in a class of models. Math. Operations-forschung Statist., Ser. Statist. 5:379–398
Pukelsheim F (1993) Optimal design of experiments. Wiley, New York
Pukelsheim F, Studden WJ (1993) E-optimal designs for polynomial regression. Ann. Statist. 21:402–415
Skibinsky M (1986) Principal representations and canonical moment sequences for distributions on an interval. J. Math. Appl. 120:95–120
Studden WJ (1968) Optimal designs on Tchebycheff points. Ann. Math. Statist. 39:1435–1447
Studden WJ (1980)D s -optimal designs for polynomial regression using continued fractions. Ann. Statist. 8:1132–1141
Studden WJ (1982) Optimal designs for weighted polynomial regression using canonical moments. In: Statistical decision theory and related topics III, Gupta SS, Berger JO (eds.) Academic Press, New York:335–350
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dette, H. A note on the uniform distribution on the arcsin points. Metrika 46, 71–82 (1997). https://doi.org/10.1007/BF02717167
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02717167