Quantile Regression of Interval-Valued Data

Linear regression is a standard statistical method widely used for prediction. It focuses on modeling the mean the target variable without accounting for all the distributional properties of this variable. In contrast, the quantile regression model facilitates the analysis of the full distributional properties, it allows to model different quantities of the target variable. This paper proposes a quantile regression model for interval data. In this model, each interval variable of the input data is represented by its range and center and a smooth function between two vectors composed by interval variables are defined. In order to test the usefulness of the proposed model, a simulation study is undertaken and an application using a scientific production interval data set of institutions from Brazil is performed. The quality of the interval prediction obtained by the proposed model is assessed by mean magnitude of relative error calculated from test data.