Regression Design for One-Dimensional Subspaces

Abstract

Consider a regression problem with univariate response y and p × 1 vector of design variables x, and assume that the cumulative distribution function F(y|x) depends on x only through the linear combination θ ^T × so that F(y|x) = F(y|θ ^T x) for all x in the design space. When the form of F is unknown, θ  is not estimable. However, under certain conditions the subspace S(θ) of R ^P spanned by θ is estimable. The goal of this paper is to begin investigating how to design an experiment so that standard methods of estimation may yield useful estimates of S(θ) when the family F(y|θ ^T x) is unknown. This may provide a baseline for assessing the robustness of designs based on an assumed family F, in addition to allowing insight into model robust design.