Open Access
August 2017 Robust discrimination designs over Hellinger neighbourhoods
Rui Hu, Douglas P. Wiens
Ann. Statist. 45(4): 1638-1663 (August 2017). DOI: 10.1214/16-AOS1503


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.


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Rui Hu. Douglas P. Wiens. "Robust discrimination designs over Hellinger neighbourhoods." Ann. Statist. 45 (4) 1638 - 1663, August 2017.


Received: 1 April 2016; Revised: 1 June 2016; Published: August 2017
First available in Project Euclid: 28 June 2017

zbMATH: 1378.62036
MathSciNet: MR3670191
Digital Object Identifier: 10.1214/16-AOS1503

Primary: 62H30 , 62K99
Secondary: 62F35

Keywords: adaptive design , Hellinger distance , Kullback–Leibler divergence , maximin , Michaelis–Menten model , Neyman–Pearson test , Nonlinear regression , optimal design , robustness , sequential design

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.45 • No. 4 • August 2017
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