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UNIFORM INFERENCE IN A GENERALIZED INTERVAL ARITHMETIC CENTER AND RANGE LINEAR MODEL
Published online by Cambridge University Press: 13 August 2021
Abstract
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Via generalized interval arithmetic, we propose a Generalized Interval Arithmetic Center and Range (GIA-CR) model for random intervals, where parameters in the model satisfy linear inequality constraints. We construct a constrained estimator of the parameter vector and develop asymptotically uniformly valid tests for linear equality constraints on the parameters in the model. We conduct a simulation study to examine the finite sample performance of our estimator and tests. Furthermore, we propose a coefficient of determination for the GIA-CR model. As a separate contribution, we establish the asymptotic distribution of the constrained estimator in Blanco-Fernández (2015, Multiple Set Arithmetic-Based Linear Regression Models for Interval-Valued Variables) in which the parameters satisfy an increasing number of random inequality constraints.
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.- Copyright
- © The Author(s), 2021. Published by Cambridge University Press
Footnotes
We are grateful to Peter C. B. Phillips, Patrik Guggenberger, and two anonymous referees for their insightful comments on the previous version of this paper. We also thank Aman Ullah, participants of the 8th International Symposium on Econometric Analysis and Forecasting at Dongbei University of Finance and Economics, statistics seminar at Northeast Normal University, the 2018 International Symposium of Quantitative Economics at Jilin University, the 2018 Seattle–Vancouver Econometrics Conference at Simon Fraser University, and seminars at University of Alberta, Korea University, Seoul National University, UC Irvine, and UC Riverside for helpful discussions. This work was facilitated by the Hyak supercomputer system at the University of Washington.
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