Modeling Regression Quantile Process Using Monotone B-Splines

ABSTRACT

Quantile regression as an alternative to conditional mean regression (i.e., least-square regression) is widely used in many areas. It can be used to study the covariate effects on the entire response distribution by fitting quantile regression models at multiple different quantiles or even fitting the entire regression quantile process. However, estimating the regression quantile process is inherently difficult because the induced conditional quantile function needs to be monotone at all covariate values. In this article, we proposed a regression quantile process estimation method based on monotone B-splines. The proposed method can easily ensure the validity of the regression quantile process and offers a concise framework for variable selection and adaptive complexity control. We thoroughly investigated the properties of the proposed procedure, both theoretically and numerically. We also used a case study on wind power generation to demonstrate its use and effectiveness in real problems. Supplementary materials for this article are available online.

KEYWORDS:

• Monotone B-splines
• Noncrossing
• Quantile regression
• Variable selection

Supplementary Materials

The PDF file provides the technical details as referred in the article. It also includes additional figures and tables from simulation studies (PDF file).

Acknowledgments

We would like to thank the editor, associate editor, and two anonymous referees for their constructive comments and suggestions that have considerably improved the article. This analysis has benefited from measurements downloaded from the Internet database: “Database of Wind Characteristics” located at DTU, Denmark (http://www.winddata.com/). Nan Chen was partially supported by Singapore AcRF funding R-266-000-085-112 and National Research Foundation Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE). Shiyu Zhou was partially supported by National Science Foundation under grant IIS-1343969 and Air Force Office of Scientific Research under grant FA9550-14-1-0384.