G-optimal Designs Research Articles

G-optimal designs for multi-factor experiments with heteroscedastic errors

We consider constructing G-optimal designs for multi-factor experiments when the errors are heteroscedastic. The method is illustrated with examples assuming the Kronecker product models and the additive models. Sufficient conditions are given so that G-optimal designs for the multi-factor experiments can be constructed from the optimal designs for the single-factor experiments.

Heteroscedastic G-Optimal Designs

SUMMARY This paper addresses the issue of constructing large sample G-optimal designs when the variability of the response varies across a compact design space. A useful characterization theorem is presented along with a computer algorithm for generating (heteroscedastic) G-optimal designs. to facilitate comparisons between D- and G-optimal designs, Atwood's inequality for comparing D- and G-efficiencies in homoscedastic models is generalized to heteroscedastic models. Some robustness properties of these designs are presented.

The Application of the Annealing Algorithm to the Construction of Exact Optimal Designs for Linear – Regression Models

This article reports the application of the annealing algorithm to the construction of exact D−, I−, and G-optimal designs for polynomial regression of degree 5 on the interval [—1, l] and for the second-order model in two factors on the design space [—1, l] × [—1, 1]. Details of the perturbation scheme and the annealing schedules used are given, and the method of implementation is illustrated by means of a simple example. The algorithm is assessed by comparing its performance, in terms of computer time and effkiency, with the modified Fedorov procedure, and it is shown to be particularly effective in finding G-optimal designs. The salient features of the exact designs constructed in this study are also summarized.

The Application of the Annealing Algorithm to the Construction of Exact Optimal Designs for Linear-Regression Models

This article reports the application of the annealing algorithm to the construction of exact D−, I−, and G-optimal designs for polynomial regression of degree 5 on the interval [—1, l] and for the second-order model in two factors on the design space [—1, l] × [—1, 1]. Details of the perturbation scheme and the annealing schedules used are given, and the method of implementation is illustrated by means of a simple example. The algorithm is assessed by comparing its performance, in terms of computer time and effkiency, with the modified Fedorov procedure, and it is shown to be particularly effective in finding G-optimal designs. The salient features of the exact designs constructed in this study are also summarized.