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Metrika

, Volume 46, Issue 1, pp 71–82 | Cite as

A note on the uniform distribution on the arcsin points

  • Holger Dette
Article

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.

Keywords and Phrases

arcsin support designs canonical moments D-efficiency 

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Copyright information

© Physica-Verlag 1997

Authors and Affiliations

  • Holger Dette
    • 1
  1. 1.Fakultät für MathematikRuhr-Universität BochumBochumGermany

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