Varying Coefficient Model via Adaptive Spline Fitting

Abstract

The varying coefficient model is a potent dimension reduction tool for nonparametric modeling and has received extensive attention from researchers. Most existing methods for fitting this model use polynomial splines with equidistant knots and treat the number of knots as a hyperparameter. However, imposing equidistant knots tends to be overly rigid, and systematically determining the optimal number of knots is also challenging. In this article, we address these challenges by employing polynomial splines with adaptively selected and predictor-specific knots to fit the varying coefficients in the model. We propose an efficient dynamic programming algorithm to find the optimal solution. Numerical results demonstrate that our new method achieves significantly smaller mean squared errors for coefficient estimations compared to the equidistant spline fitting method. An implementation of our method in R is available at https://github.com/wangxf0106/vcmasf. Proofs of the theorems are provided in the online supplementary materials.

Keywords:

• Mean squared error
• Splines and knots
• Varying coefficient model

Acknowledgments

We would like to express our sincere gratitude to the National Oceanic and Atmospheric Administration Regional Climate Centers, especially the Northeast Regional Climate Center at Cornell University, for their generous cooperation and sharing of the meteorological data used in this study. We are also thankful to the Environmental Protection Agency and the Department of Health, New York State, for providing access to the air quality data and daily infected records, which were invaluable for our research.

Disclosure Statement

There are no competing interests to declare.

Additional information

Funding

We acknowledge the support received from the NSF grant DMS-2015411 and DMS-1903139, which played a crucial role in funding and supporting this research project. Their financial assistance has greatly contributed to the successful completion of this work.