Saturated locally optimal designs under differentiable optimality criteria

TL;DR

This paper develops a general theoretical framework for identifying saturated locally optimal experimental designs in single-covariate models using differentiable optimality criteria, extending previous class results.

Contribution

It introduces new tools for finding saturated optimal designs and proves their uniqueness under mild conditions, filling a gap in design theory.

Findings

Saturated optimal designs exist under the studied models.

The paper provides methods to find these designs.

Uniqueness of saturated optimal designs is established.

Abstract

We develop general theory for finding locally optimal designs in a class of single-covariate models under any differentiable optimality criterion. Yang and Stufken [Ann. Statist. 40 (2012) 1665-1681] and Dette and Schorning [Ann. Statist. 41 (2013) 1260-1267] gave complete class results for optimal designs under such models. Based on their results, saturated optimal designs exist; however, how to find such designs has not been addressed. We develop tools to find saturated optimal designs, and also prove their uniqueness under mild conditions.