fastkqr: A Fast Algorithm for Kernel Quantile Regression

Quantile regression (Koenker and Bassett, 1978) is a popular tool in statistics and econometrics. The method extends median regression from fitting the conditional median to modeling a suite of conditional quantile functions, providing a more comprehensive and nuanced view of the relationship between a response variable and its predictors. One of the key advantages of quantile regression, also rooted in median regression, is its robustness against outliers in the response direction. Since its introduction, quantile regression has been adapted in various research areas, including survival analysis (Peng and Huang, 2008; Wang and Wang, 2009), longitudinal data modeling (Koenker, 2004), machine learning (Meinshausen and Ridgeway, 2006; Fakoor et al., 2023), and so on, and has seen widespread applications in fields such as finance, ecology, healthcare, and engineering. For detailed introductions and the latest developments in quantile regression, see Koenker (2017) and Koenker et al. (2018). Despite its popularity, one primary limitation of quantile regression is its high computational cost, which is also inherited from its median regression origins.