Quantile regression for compositional covariates

Quantile regression is a very important tool to explore the relationship between response variable and its covariates. Motivated by mean with LASSO for compositional covariates proposed Lin et al. (Biometrika 101 (4):785–97, 2014), we consider quantile no-penalty penalty function. We develop computational algorithms based on linear programming. Numerical studies indicate that our methods provide better alternative than under many settings, particularly heavy-tailed or skewed distribution of error term. Finally, study fat data using method.