A note on the uniform distribution on the arcsin points |
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Authors: | Holger Dette |
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Institution: | 1. Fakult?t für Mathematik, Ruhr-Universit?t Bochum, Universit?tsstr. 150, D-44780, Bochum, Germany
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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. |
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Keywords: | arcsin support designs canonical moments D-efficiency |
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