Robust Designs Based on the Infinitesimal Approach

Abstract

We introduce an infinitesimal approach to the construction of robust designs for linear models. The resulting designs are robust against small departures from the assumed linear regression response and/or small departures from the assumption of uncorrelated errors. Subject to satisfying a robustness constraint, they minimize the determinant of the mean squared error matrix of the least squares estimator at the ideal model. The robustness constraint is quantified in terms of boundedness of the Gateaux derivative of this determinant, in the direction of a contaminating response function or autocorrelation structure. Specific examples are considered. If the aforementioned bounds are sufficiently large, then (permutations of) the classically optimal designs, which minimize variance alone at the ideal model, meet our robustness criteria. Otherwise, new designs are obtained.

Key Words:

• Approximately linear regression response
• B robustness
• M robustness
• Regression design
• V robustness.