The Annals of Statistics

Robust discrimination designs over Hellinger neighbourhoods

Rui Hu and Douglas P. Wiens

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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.

Article information

Source
Ann. Statist., Volume 45, Number 4 (2017), 1638-1663.

Dates
Received: April 2016
Revised: June 2016
First available in Project Euclid: 28 June 2017

Permanent link to this document
https://projecteuclid.org/euclid.aos/1498636869

Digital Object Identifier
doi:10.1214/16-AOS1503

Mathematical Reviews number (MathSciNet)
MR3670191

Zentralblatt MATH identifier
1378.62036

Subjects
Primary: 62K99: None of the above, but in this section 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20]
Secondary: 62F35: Robustness and adaptive procedures

Keywords
Adaptive design Hellinger distance Kullback–Leibler divergence maximin Michaelis–Menten model Neyman–Pearson test nonlinear regression optimal design robustness sequential design

Citation

Hu, Rui; Wiens, Douglas P. Robust discrimination designs over Hellinger neighbourhoods. Ann. Statist. 45 (2017), no. 4, 1638--1663. doi:10.1214/16-AOS1503. https://projecteuclid.org/euclid.aos/1498636869


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Supplemental materials

  • Supplement to “Robust discrimination designs over Hellinger neighbourhoods”. There we give the rather lengthy proof of Theorem 2.1, which depends on a number of preliminary lemmas. We also show that the conditions of this theorem apply to normal and log-normal densities.