A note on the uniform distribution on the arcsin points
In his book Pukelsheim  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.
Keywords and Phrasesarcsin support designs canonical moments D-efficiency
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