Locally $D$-optimal Designs for Non-linear Models on the $k$-dimensional Ball

TL;DR

This paper develops methods for constructing locally D-optimal experimental designs for various non-linear regression models within a k-dimensional ball, utilizing invariance principles, and extends these results to ellipsoids.

Contribution

It introduces a novel approach using invariance and equivariance to find D-optimal designs for non-linear models on spherical and ellipsoidal regions.

Findings

Constructed D-optimal designs for Poisson, negative binomial, and proportional hazard models.

Extended the design methodology from spherical to ellipsoidal regions.

Demonstrated the effectiveness of invariance-based design construction.

Abstract

In this paper we construct (locally) $D$-optimal designs for a wide class of non-linear multiple regression models, when the design region is a $k$-dimensional ball. For this construction we make use of the concept of invariance and equivariance in the context of optimal designs. As examples we consider Poisson and negative binomial regression as well as proportional hazard models with censoring. By generalisation we can extend these results to arbitrary ellipsoids.