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

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.