A Quadratic Design Criterion for Precise Estimation in Nonlinear Regression Models

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Abstract
D-optimal experimental designs for precise estimation in nonlinear regression models are obtained by minimizing the determinant of the approximate variance–covariance matrix of the parameter estimates. This determinant may not give a true indication of the volume of a joint inference region for the parameters, however, because of intrinsic and parameter-effects nonlinearity. In this article, we investigate experimental designs that minimize a second-order volume approximation. Unlike D-optimal designs, these designs depend on the noise and confidence levels, and on the parameterization used, and when used sequentially, quadratic designs depend on the residuals from previous experiments and on the type of inference. Quadratic designs appear to be less sensitive to variations in initial parameter values used for design.

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