Department of Statistics, Tarbiat Modares University, Tehran, Iran.
J Biopharm Stat. 2024 May;34(3):297-322. doi: 10.1080/10543406.2023.2198593. Epub 2023 Apr 9.
Quantile regression has recently received a considerable attention due to its remarkable development in enriching the variety of regression models. Many efforts have been made to blend different penalty and loss function to extend or develop novel regression models that are unique from different perspectives. Bearing in mind that the lasso quantile regression model ignores the randomness of the realizations in the penalty part, we propose a new penalty for the quantile regression models. Similar to the adaptive lasso quantile regression model, the proposed model simultaneously does estimation and variable selection tasks. We call the new model 'lqsso-QR', standing for the least quantile shrinkage and selection operator quantile regression. In this article, we present a sufficient and necessary condition for the variable selection of the lasso quantile regression to enjoy the consistent property. We show that the lqsso-QR follows oracle properties under some mild conditions. From computational perspective, we apply an efficient algorithm, originally developed for the lasso quantile regression. Using simulation studies, we elaborate on the superiority of the proposed model compared with other lasso-type penalties, especially regarding relative prediction error. Also, an application of our method to a real-life data; the rat eye data, is reported.
分位数回归由于其在丰富回归模型种类方面的显著发展，最近受到了相当多的关注。人们已经做出了许多努力，将不同的惩罚和损失函数融合在一起，以扩展或开发从不同角度来看独特的新型回归模型。考虑到lasso 分位数回归模型忽略了惩罚部分中实现的随机性，我们为分位数回归模型提出了一种新的惩罚。类似于自适应lasso 分位数回归模型，所提出的模型同时执行估计和变量选择任务。我们将新模型称为“lqsso-QR”，代表最小分位数收缩和选择算子分位数回归。在本文中，我们给出了 lasso 分位数回归进行变量选择以享受一致性属性的充分必要条件。我们表明，在一些温和的条件下，lqsso-QR 遵循 oracle 属性。从计算的角度来看，我们应用了一种最初为 lasso 分位数回归开发的有效算法。通过模拟研究，我们详细说明了与其他 lasso 型惩罚相比，该模型的优越性，尤其是在相对预测误差方面。此外，还报告了我们的方法在真实数据——老鼠眼睛数据上的应用。
