June 2022 Confidence regions near singular information and boundary points with applications to mixed models
Karl Oskar Ekvall, Matteo Bottai
Author Affiliations +
Ann. Statist. 50(3): 1806-1832 (June 2022). DOI: 10.1214/22-AOS2177


We propose confidence regions with asymptotically correct uniform coverage probability of parameters whose Fisher information matrix can be singular at important points of the parameter set. Our work is motivated by the need for reliable inference on scale parameters close or equal to zero in mixed models, which is obtained as a special case. The confidence regions are constructed by inverting a continuous extension of the score test statistic standardized by expected information, which we show exists at points of singular information under regularity conditions. Similar results have previously only been obtained for scalar parameters, under conditions stronger than ours, and applications to mixed models have not been considered. In simulations our confidence regions have near-nominal coverage with as few as n=20 observations, regardless of how close to the boundary the true parameter is. It is a corollary of our main results that the proposed test statistic has an asymptotic chi-square distribution with degrees of freedom equal to the number of tested parameters, even if they are on the boundary of the parameter set.


The authors thank two referees and an Associate Editor for comments that helped improve the manuscript substantially.


Download Citation

Karl Oskar Ekvall. Matteo Bottai. "Confidence regions near singular information and boundary points with applications to mixed models." Ann. Statist. 50 (3) 1806 - 1832, June 2022. https://doi.org/10.1214/22-AOS2177


Received: 1 March 2021; Revised: 1 January 2022; Published: June 2022
First available in Project Euclid: 16 June 2022

MathSciNet: MR4441141
zbMATH: 07547951
Digital Object Identifier: 10.1214/22-AOS2177

Primary: 62F05 , 62F25
Secondary: 62J05

Keywords: boundary points , Confidence regions , mixed models , Singular information

Rights: Copyright © 2022 Institute of Mathematical Statistics


This article is only available to subscribers.
It is not available for individual sale.

Vol.50 • No. 3 • June 2022
Back to Top