Abstract
An optimal design concentrated at a minimum number of points is considered for a polynomial regression experiment on the sphere. For the case of a polynomial experiment on the circle it is possible to explicitly find the parameters of an optimal minimal design if any optimal design is known.
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Literature cited
S. Karlin and W. J. Studden, “Optimal experimental designs,” Annals Math. Stat.,37, 4 (1966).
J. Kiefer, “Optimal experimental designs. V. With applications to systematic and rotatable designs,” in: Proc. Fourth Berkeley Symposium, Vol. 1, University of California Press, Berkeley, California (1960).
R. H. Farrell, J. Kiefer, and A. Walbran, “Optimum multivariate designs, in: Proc. Fifth Berkeley Sympos. Math. Stat. and Probab., 1965–1966, Vol. 1, Berkeley-Los Angeles (1967).
B. L. Granovskii, “Construction of optimal rotatable designs for the circle,” Abstracts of Reports Fourth All-Union Conference on Scientific Experiment Planning and Automation, Moscow (1973).
V. I. Krylov, Approximate Calculation of Integrals [in Russian], Moscow (1967).
N. Akhiezer and M. Krein, Problems of the Theory of Moments [in Russian], GONTI, Kharkov (1938).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 53, pp. 107–117, 1975.
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Granovskii, B.L. A method of construction of optimal experimental designs for the circle. J Math Sci 12, 218–226 (1979). https://doi.org/10.1007/BF01262720
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DOI: https://doi.org/10.1007/BF01262720