There is a growing need for the ability to analyse interval-valued data. However, existing descriptive frameworks to achieve this ignore the process by which interval-valued data are typically constructed; namely by the aggregation of real-valued data generated from some underlying process. In this article we develop the foundations of likelihood based statistical inference for random intervals that directly incorporates the underlying generative procedure into the analysis. That is, it permits the direct fitting of models for the underlying real-valued data given only the random interval-valued summaries. This generative approach overcomes several problems associated with existing methods, including the rarely satisfied assumption of within-interval uniformity. The new methods are illustrated by simulated and real data analyses.

中文翻译：

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构造区间值随机变量的似然函数

对分析区间值数据的能力的需求日益增长。然而，实现这一目标的现有描述框架忽略了通常构造区间值数据的过程；即通过聚合从某些底层过程生成的实值数据。在本文中，我们为随机区间开发了基于似然的统计推理的基础，这些随机区间将潜在的生成程序直接纳入分析。也就是说，它允许仅给定随机区间值摘要的基础实值数据直接拟合模型。这种生成方法克服了与现有方法相关的几个问题，包括很少满足的区间内均匀性假设。通过模拟和真实数据分析来说明新方法。