A New Characterization of Elfving's Method for High Dimensional Computation

TL;DR

This paper introduces a new explicit characterization of Elfving's method for high-dimensional c-optimal design computation, simplifying the process by reducing it to a single optimization problem and demonstrating its application in polynomial and logistic regression models.

Contribution

It provides explicit formulas for optimal weights and signs, eliminating the need for parameter search in Elfving's method, thus streamlining high-dimensional design computation.

Findings

Explicit formulas for optimal weights and signs in Elfving's method

Reduced computational complexity to a single optimization problem

Successful application to polynomial and logistic regression models

Abstract

We give a new characterization of Elfving's (1952) method for computing c-optimal designs in k dimensions which gives explicit formulae for the k unknown optimal weights and k unknown signs in Elfving's characterization. This eliminates the need to search over these parameters to compute c-optimal designs, and thus reduces the computational burden from solving a family of optimization problems to solving a single optimization problem for the optimal finite support set. We give two illustrative examples: a high dimensional polynomial regression model and a logistic regression model, the latter showing that the method can be used for locally optimal designs in nonlinear models as well.