Robust designs for approximately linear regression: \(M\)-estimated parameters
The author considers a parameter-linear regression model \(y_ i= \Theta^ T u(x_ i)+ f(x_ i)+ \varepsilon_ i\), \(i=1, \dots, n\); with model contamination \(f(x_ i)\). Usually, robustness of estimation and design robustness against model deviations are considered separately. An advantage of the paper under review is that it presents a common approach: For Huber's \(M\)-estimators and parametric contamination \(f_ \alpha(x):= \alpha^ T \nu(x)\) with given \(\nu(x)\), the author investigates the designing problem where as loss function a sum of asymptotic variances, bias and model misspecification is used. Especially minimax rotatable designs are derived for multiple linear regression with quadratic contamination, subject to a lower bound on the power of a robust test of the hypothesis \(\alpha=0\). The optimal designs place their mass at the centre of the design space, and on a sphere interior to the design space.
design robustness against model deviations
sum of asymptotic variances, bias and model misspecification
scientific article; zbMATH DE number 605339
scientific article