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 $\lbrack a, b\rbrack$ 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 $\lbrack -b, b\rbrack$ for certain subparameters, provided the region is "small enough," for example, $b \leq 1$. In particular, by specializing the weight function, we obtain results of Pukelsheim and Studden and of Dette.
Citation
Berthold Heiligers. "$E$-Optimal Designs in Weighted Polynomial Regression." Ann. Statist. 22 (2) 917 - 929, June, 1994. https://doi.org/10.1214/aos/1176325503
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