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

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

2011-05-18

arxiv.org/abs/1105.3575v1

Annals of Statistics 2011, Vol. 39, No. 2, 1266-1281

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/11-AOS875 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/11-AOS875

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.

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