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.

通过广义区间算法，我们提出了一个用于随机区间的广义区间算术中心和范围 (GIA-CR) 模型，其中模型中的参数满足线性不等式约束。我们构建了参数向量的约束估计器，并对模型中参数的线性等式约束开发了渐近一致有效的测试。我们进行了一项模拟研究，以检查我们的估算器和测试的有限样本性能。此外，我们还提出了 GIA-CR 模型的决定系数。作为一项单独的贡献，我们在 Blanco-Fernández（2015 年，区间值变量的多组基于算术的线性回归模型）中建立了约束估计量的渐近分布，其中参数满足越来越多的随机不等式约束。