Quantile regression for compositional covariates

TL;DR

This paper develops quantile regression methods for compositional covariates, offering computational algorithms and demonstrating improved performance over mean regression, especially with heavy-tailed or skewed errors.

Contribution

It introduces quantile regression with and without penalty for compositional data, along with efficient linear programming algorithms.

Findings

Better performance than mean regression in various settings

Effective with heavy-tailed and skewed error distributions

Applied successfully to fat data analysis

Abstract

Quantile regression is a very important tool to explore the relationship between the response variable and its covariates. Motivated by mean regression with LASSO for compositional covariates proposed by Lin et al. (2014), we consider quantile regression with no-penalty and penalty function. We develop the computational algorithms based on linear programming. Numerical studies indicate that our methods provides the better alternative than mean regression under many settings, particularly for heavy-tailed or skewed distribution of the error term. Finally, we study the fat data using the proposed method.