Robust discrimination designs over Hellinger neighbourhoods
The Annals of Statistics · 2017 · Volume 45 · Issue 4
Abstract
To aid in the discrimination between two, possibly nonlinear, regression models, we study the construction of experimental designs. Considering that each of these two models might be only approximately specified, robust “maximin” designs are proposed. The rough idea is as follows. We impose neighbourhood structures on each regression response, to describe the uncertainty in the specifications of the true underlying models. We determine the least favourable—in terms of Kullback–Leibler divergence—members of these neighbourhoods. Optimal designs are those maximizing this minimum divergence. Sequential, adaptive approaches to this maximization are studied. Asymptotic optimality is established.
Keywords
62F35, 62H30, 62K99, adaptive design, Hellinger distance, Kullback–Leibler divergence, maximin, Michaelis–Menten model, Neyman–Pearson test, Nonlinear regression, optimal design, robustness, sequential design
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