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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Abstract

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

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

Dates
First available in Project Euclid: 9 May 2011

Permanent link to this document
https://projecteuclid.org/euclid.aos/1304947050

Digital Object Identifier
doi:10.1214/11-AOS875

Mathematical Reviews number (MathSciNet)
MR2816354

Zentralblatt MATH identifier
1216.62113

Subjects
Primary: 62K05: Optimal designs

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

Citation

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. https://projecteuclid.org/euclid.aos/1304947050


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