Various Optimality Criteria for the Prediction of Individual Response Curves

TL;DR

This paper investigates optimal experimental design criteria, including Kiefer's and G-criteria, for predicting individual response curves in fixed effects and random coefficients regression models, providing theoretical insights and equivalence results.

Contribution

It extends Kiefer's optimality criteria to approximate designs and establishes the equivalence of E-criteria across fixed effects and RCR models, with detailed analysis of the G-criterion.

Findings

Derived general Kiefer criteria for approximate designs

Proved equivalence of E-criteria in fixed effects and RCR models

Analyzed G-criterion for linear regression in specific regions

Abstract

We consider optimal designs for the Kiefer cirteria, which include the E-criterion as a particular case, and the G-criterion in random coefficients regression (RCR) models. We obtain general the Kiefer criteria for approximate designs and prove the equivalence of the E-criteria in the fixed effects and RCR models. We discuss in detail the G-criterion for ordinary linear regression on specific design regions.