Minimax Regression Designs Under Uniform Departure Models

Abstract

Model robustness in optimal regression design is studied by introducing a family of nonparametric models, which are defined as neighborhoods of classical parametric models in terms of the uniform norm. Optimal designs are sought under a minimax criterion for estimating linear functionals on such models that may be put as integrals using measures of finite support. A set of conditions equivalent to design optimality is derived using a Lagrangian principle applicable when the dimension is infinite and the function is not everywhere differentiable. From these conditions various optimal designs follow. Among them is the classical extrapolation design of Kiefer and Wolfowitz for Chebyshev regression, which is therefore model-robust against uniform departure. The conditions also shed light on other classical results of Kiefer and Wolfowitz and of others.