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A note on the de la Garza phenomenon for locally optimal designs

18 May 2011
Holger Dette
V. Melas
ArXiv (abs)PDFHTML
Abstract

The celebrated de la Garza phenomenon states that for a polynomial regression model of degree p−1p-1p−1 any optimal design can be based on at most ppp design points. In a remarkable paper, Yang [Ann. Statist. 38 (2010) 2499--2524] showed that this phenomenon exists in many locally optimal design problems for nonlinear models. In the present note, we present a different view point on these findings using results about moment theory and Chebyshev systems. In particular, we show that this phenomenon occurs in an even larger class of models than considered so far.

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