Abstract

The reciprocal LASSO estimate for linear regression corresponds to a posterior mode when independent inverse Laplace priors are assigned on the regression coefficients. This paper studies reciprocal LASSO in quantile regression from a Bayesian perspective. Simple and efficient Gibbs sampling algorithms are developed for posterior inference using a scale mixture of inverse uniforms (or double Pareto densities), which can be further decomposed as a scale mixture of truncated normals. Slight modifications of this approach lead to Bayesian analogues of other related estimation methods, including reciprocal adaptive LASSO, reciprocal bridge, and reciprocal adaptive bridge. Empirical evidence of the attractiveness of the method is demonstrated via extensive simulation studies and two real data applications. Results show that the proposed methods perform quite well under a variety of scenarios.

摘要

当在回归系数上分配独立的逆拉普拉斯先验时，线性回归的倒数 LASSO 估计对应于后验模式。本文从贝叶斯的角度研究分位数回归中的倒数 LASSO。使用逆均匀（或双 Pareto 密度）的尺度混合，为后验推断开发了简单有效的 Gibbs 采样算法，可以进一步分解为截断法线的尺度混合。这种方法的轻微修改导致其他相关估计方法的贝叶斯类似物，包括互惠自适应 LASSO、互惠桥和互惠自适应桥。通过广泛的模拟研究和两个真实数据应用证明了该方法的吸引力的经验证据。