This paper proposes a new method to address the long-standing problem of lack of monotonicity in estimation of the conditional and structural quantile function, also known as quantile crossing problem. Quantile regression is a very powerful tool in data science in general and econometrics in particular. Unfortunately, the crossing problem has been confounding researchers and practitioners alike for over 4 decades. Numerous attempts have been made to find a simple and general solution. This paper describes a unique and elegant solution to the problem based on a flexible check function that is easy to understand and implement in R and Python, while greatly reducing or even eliminating the crossing problem entirely. It will be very important in all areas where quantile regression is routinely used and may also find application in robust regression, especially in the context of machine learning. From this perspective, we also utilize the flexible check function to provide insights into the root causes of the crossing problem.
翻译:本文提出了一种新的方法,以解决长期存在的在估计有条件的和结构性的四分位函数方面缺乏单一性的问题,也称为孔径交叉问题。量化回归是一般数据科学和具体计量数据科学中非常有力的工具。不幸的是,过去40多年来,跨度问题一直困扰着研究人员和从业者。为了找到一个简单和普遍的解决办法,已经做出了许多尝试。本文件描述了一种独特和优雅的解决问题的办法,其基础是便于理解和在R和Python执行的灵活检查功能,同时大大地减少甚至完全消除跨度问题。这对于通常使用孔径回归的所有地区都非常重要,而且也可能在稳健的回归中找到应用,特别是在机器学习方面。从这个角度看,我们还利用灵活检查功能来深入了解跨度问题的根源。