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December 2019 On optimal designs for nonregular models
Yi Lin, Ryan Martin, Min Yang
Ann. Statist. 47(6): 3335-3359 (December 2019). DOI: 10.1214/18-AOS1780

Abstract

Classically, Fisher information is the relevant object in defining optimal experimental designs. However, for models that lack certain regularity, the Fisher information does not exist, and hence, there is no notion of design optimality available in the literature. This article seeks to fill the gap by proposing a so-called Hellinger information, which generalizes Fisher information in the sense that the two measures agree in regular problems, but the former also exists for certain types of nonregular problems. We derive a Hellinger information inequality, showing that Hellinger information defines a lower bound on the local minimax risk of estimators. This provides a connection between features of the underlying model—in particular, the design—and the performance of estimators, motivating the use of this new Hellinger information for nonregular optimal design problems. Hellinger optimal designs are derived for several nonregular regression problems, with numerical results empirically demonstrating the efficiency of these designs compared to alternatives.

Citation

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Yi Lin. Ryan Martin. Min Yang. "On optimal designs for nonregular models." Ann. Statist. 47 (6) 3335 - 3359, December 2019. https://doi.org/10.1214/18-AOS1780

Information

Received: 1 February 2018; Revised: 1 October 2018; Published: December 2019
First available in Project Euclid: 31 October 2019

Digital Object Identifier: 10.1214/18-AOS1780

Subjects:
Primary: 62K05
Secondary: 62B10

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 6 • December 2019
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