This paper extends the idea of decoupling shrinkage and sparsity for continuous priors to Bayesian Quantile Regression (BQR). The procedure follows two steps: In the first step, we shrink the quantile regression posterior through state of the art continuous priors and in the second step, we sparsify the posterior through an efficient variant of the adaptive lasso, the signal adaptive variable selection (SAVS) algorithm. We propose a new variant of the SAVS which automates the choice of penalisation through quantile specific loss-functions that are valid in high dimensions. We show in large scale simulations that our selection procedure decreases bias irrespective of the true underlying degree of sparsity in the data, compared to the un-sparsified regression posterior. We apply our two-step approach to a high dimensional growth-at-risk (GaR) exercise. The prediction accuracy of the un-sparsified posterior is retained while yielding interpretable quantile specific variable selection results. Our procedure can be used to communicate to policymakers which variables drive downside risk to the macro economy.

翻译：本文扩展了对巴伊西亚量子回归( BQR) 连续前科进行缩缩和宽度分离的想法。 程序分为两步: 第一步, 我们通过最先进的连续前科和第二步, 缩小四分位回归后部, 我们通过适应性拉索( SAVS) 信号适应性变量选择算法( SAVS) 的有效变体, 将后部放大。 我们提出了SAVS 的一个新变体, 该变体通过高度有效的量化特定损失函数自动选择处罚。 我们用大规模模拟显示, 我们的选择程序会降低偏差, 而不考虑数据中真正潜在的宽度, 与未分化的回归后部相比。 我们用两步法对高维增长风险( GaIR) 演算。 未分解的后部位值的预测准确性会保留下来, 同时产生可解释的量化具体变量选择结果。 我们的程序可以用来向决策者传递变量, 将变量推向下向宏观经济。