The Annals of Statistics

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

Holger Dette and Viatcheslav B. Melas

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The celebrated de la Garza phenomenon states that for a polynomial regression model of degree p−1 any optimal design can be based on at most p 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.

Article information

Ann. Statist., Volume 39, Number 2 (2011), 1266-1281.

First available in Project Euclid: 9 May 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62K05: Optimal designs

Locally optimal designs saturated designs complete class theorem moment spaces Chebyshev systems


Dette, Holger; Melas, Viatcheslav B. A note on the de la Garza phenomenon for locally optimal designs. Ann. Statist. 39 (2011), no. 2, 1266--1281. doi:10.1214/11-AOS875.

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