The Mean Squared Error Optimum Design Criterion for Parameter Estimation in Nonlinear Regression Models

Abstract

In the context of nonlinear regression models, we propose an optimal experimental design criterion for estimating the parameters that account for the intrinsic and parameter-effects nonlinearity. The optimal design criterion proposed in this article minimizes the determinant of the mean squared error matrix of the parameter estimator that is quadratically approximated using the curvature array. The design criterion reduces to the D-optimal design criterion if there are no intrinsic and parameter-effects nonlinearity in the model, and depends on the scale parameter estimator and on the reparameterization used. Some examples, using a well known nonlinear kinetics model, demonstrate the application of the proposed criterion to nonsequential design of experiments as compared with the D-optimal criterion.

Keywords:

• D-optimality
• Intrinsic or parameter-effects nonlinearity
• Locally optimal designs
• Quadratic approximation
• Reparameterization

Mathematics Subject Classification:

• Primary 62K05, 65C60, 65D17
• Secondary 46N55, 90C30, 94C30