Two-sample tests for interval-valued data

Methods to compare two samples of interval-valued data are discussed. In the interval-valued data, observations have the form of intervals and are often read as two-dimensional vector of lower and upper bounds. We consider four methods, two of which are the applications of existing methods for bivariate data, and the other two are based on the marginalization (univariate distributional representation) of the interval-valued data. We conduct a comprehensive numerical study and analysis of real data to understand the performance of four methods.