D-Optimal Designs for Hierarchical Linear Models with Heteroscedastic Errors

Abstract

This paper investigates the optimal design problem for the prediction of the individual parameters in hierarchical linear models with heteroscedastic errors. An equivalence theorem is established to characterize D-optimality of designs for the prediction based on the mean squared error matrix. The admissibility of designs is also considered and a sufficient condition to simplify the design problem is obtained. The results obtained are illustrated in terms of a simple linear model with random slope and heteroscedastic errors.

Keywords

D-optimal design / Heteroscedasticity / Mean squared error matrix / Mixed-effect model / Equivalence theorem / Admissibility

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Funding

Innovative Research Group Project of the National Natural Science Foundation of China(11871143)

National Natural Science Foundation of China(11971318)

Shanghai Rising-Star Program(20QA1407500)