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 an acceptable solution but no simple and general solution has been found to date. This paper describes an elegant solution to the problem which is based on a single mathematical equation that is easy to understand and implement in R and Python, while greatly reducing the crossing problem. 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.

翻译：本文提出了一种新方法,以解决长期存在的在估计有条件的和结构性的量化功能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,特别是计量经济学方面一个非常有力的工具。不幸的是,跨度问题在40多年来一直困扰着研究人员和从业者。许多尝试都试图找到一个可以接受的解决办法,但迄今还没有找到简单和一般的解决办法。本文描述了一种优雅的解决问题的办法,它基于一个在R和Python易于理解和实施的单一数学方程式,同时大大缓解了跨度问题。这对于通常使用孔径回归的所有领域都非常重要,而且可能用于稳健的回归,特别是在机器学习方面。