Interval-valued scalar-on-function linear quantile regression based on the bivariate center and radius method.

Interval-valued functional data, a new type of data in symbolic data analysis, depicts the characteristics of a variety of big data and has drawn the attention of many researchers. Mean regression is one of the important methods for analyzing interval-valued functional data. However, this method is sensitive to outliers and may lead to unreliable results. As an important complement to mean regression, this paper proposes an interval-valued scalar-on-function linear quantile regression model. Specifically, we constructed two linear quantile regression models for the interval-valued response and interval-valued functional regressors based on the bivariate center and radius method. The proposed model is more robust and efficient than mean regression methods when the data contain outliers as well as the error does not follow the normal distribution. Numerical simulations and real data analysis of a climate dataset demonstrate the effectiveness and superiority of the proposed method over the existing methods.