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E-Optimal Designs in Weighted Polynomial Regression

Berthold Heiligers
The Annals of Statistics
Vol. 22, No. 2 (Jun., 1994), pp. 917-929
Stable URL: http://www.jstor.org/stable/2242298
Page Count: 13
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E-Optimal Designs in Weighted Polynomial Regression
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Abstract

Based on a duality between E-optimality for (sub-) parameters in weighted polynomial regression and a nonlinear approximation problem of Chebyshev type, in many cases the optimal approximate designs on nonnegative and nonpositive experimental regions [ a, b] are found to be supported by the extrema of the only equioscillating weighted polynomial over this region with leading coefficient 1. A similar result is stated for regression on symmetric regions [ -b, b] for certain subparameters, provided the region is "small enough," for example, b ≤ 1. In particular, by specializing the weight function, we obtain results of Pukelsheim and Studden and of Dette.

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