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

TL;DR

This paper explores the de la Garza phenomenon in optimal design theory, showing it applies to a broader class of models using moment theory and Chebyshev systems, extending previous results.

Contribution

It provides a new perspective on the phenomenon, demonstrating its occurrence in more models than previously known through moment theory and Chebyshev systems.

Findings

The de la Garza phenomenon applies to a larger class of models.

Moment theory and Chebyshev systems explain the phenomenon.

The results extend previous understanding of optimal design.

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.