ON OPTIMAL DESIGNS FOR NONREGULAR MODELS

• 成果类型: Article
• 署名作者: Lin, Yi; Martin, Ryan; Yang, Min
• 署名单位: University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; North Carolina State University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/18-AOS1780
• 发表日期: 2019
• 页码: 3335-3359
• 关键词: optimal discrimination designs; locally optimal designs; nonlinear models; likelihood estimation; regression; inference; robust

摘要

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.