UNIFORM INFERENCE IN A GENERALIZED INTERVAL ARITHMETIC CENTER AND RANGE LINEAR MODEL

Yanqin Fan and Xuetao Shi

Econometric Theory, 2023, vol. 39, issue 1, 27-69

Abstract: 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.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:cup:etheor:v:39:y:2023:i:1:p:27-69_2

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