Some Model Robust Designs in Regression

Abstract

Theory for finding designs in estimating a linear functional of a regression function is developed for classes of regression functions which are infinite dimensional. These classes can be viewed as representing possible departures from an "ideal" simple model and thus describe a model robust setting. The estimates are restricted to be linear and the design (and estimate) sought is minimax for mean square error. The structure of the design is obtained in a variety of cases; some asymptotic theory is given when the functionals are integrals. As to be expected, optimal designs depend critically on the particular functional to be estimated. The associated estimate is generally not a least squares estimate but we note some examples where a least squares estimate, in conjunction with a good design, is adequate.