This article considers a bent-cable quantile regression model that comprises two linear segments but is smoothly jointed by quadratic bend. very flexible to allow the relationship between response variable and covariate of interest change gradually or abruptly across point value in covariate. However, due non-differentiability objective function regression, it challenge estimate unknown paramet...

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 provid...