Solution to the Non-Monotonicity and Crossing Problems in Quantile Regression
This solves a persistent issue for researchers and practitioners in data science and econometrics, offering a general solution to improve reliability in applications like robust regression and machine learning.
The paper tackles the long-standing quantile crossing problem in quantile regression by proposing a new method based on a flexible check function, which greatly reduces or eliminates crossing and is easy to implement in R and Python.
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.