2021/11/08 by Resve Saleh, Saleh, Resve A., A. K. Md. Ehsanes Saleh +2
Decision Sciences · Engineering · Mathematics · #Advanced Statistical Methods and Models #Control Systems and Identification #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Multi-Criteria Decision Making #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2111.04805
openalex publication_date 2021/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper proposes a new method to address the long-standing problem of lack\nof monotonicity in estimation of the conditional and structural quantile\nfunction, also known as quantile crossing problem. Quantile regression is a\nvery powerful tool in data science in general and econometrics in particular.\nUnfortunately, the crossing problem has been confounding researchers and\npractitioners alike for over 4 decades. Numerous attempts have been made to\nfind a simple and general solution. This paper describes a unique and elegant\nsolution to the problem based on a flexible check function that is easy to\nunderstand and implement in R and Python, while greatly reducing or even\neliminating the crossing problem entirely. It will be very important in all\nareas where quantile regression is routinely used and may also find application\nin robust regression, especially in the context of machine learning. From this\nperspective, we also utilize the flexible check function to provide insights\ninto the root causes of the crossing problem.\n