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. (Biometrika 101 (4):785–97, 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 provide 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.

摘要

分位数回归是探索响应变量与其协变量之间关系的非常重要的工具。受林等人提出的组成协变量的 LASSO 均值回归的启发。( Biometrika 101 (4):785–97, 2014)，我们考虑具有无惩罚和惩罚函数的分位数回归。我们开发了基于线性规划的计算算法。数值研究表明，在许多设置下，我们的方法提供了比均值回归更好的替代方法，特别是对于误差项的重尾分布或偏态分布。最后，我们使用所提出的方法研究脂肪数据。