Distance-Based Analysis with Quantile Regression Models

Non-standard structured, multivariate data are emerging in many research areas, including genetics and genomics, ecology, and social science. Suitably defined pairwise distance measures are commonly used in distance-based analysis to study the association between the variables. In this work, we consider a linear quantile regression model for pairwise distances. We investigate the large sample properties of an estimator of the unknown coefficients and propose statistical inference procedures correspondingly. Extensive simulations provide evidence of satisfactory finite sample properties of the proposed method. Finally, we applied the method to a microbiome association study to illustrate its utility.