Varying Coefficient Model via Adaptive Spline Fitting

TL;DR

This paper introduces an adaptive spline fitting approach for varying coefficient models, allowing predictor-specific knots and improving estimation accuracy over traditional methods with fixed knots.

Contribution

It proposes a dynamic programming algorithm for selecting predictor-specific knots in spline-based varying coefficient models, enhancing flexibility and accuracy.

Findings

Achieves significantly lower mean squared errors compared to equidistant spline methods.

Demonstrates the effectiveness of adaptive knot selection through numerical experiments.

Abstract

The varying coefficient model has received broad attention from researchers as it is a powerful dimension reduction tool for non-parametric modeling. Most existing varying coefficient models fitted with polynomial spline assume equidistant knots and take the number of knots as the hyperparameter. However, imposing equidistant knots appears to be too rigid, and determining the optimal number of knots systematically is also a challenge. In this article, we deal with this challenge by utilizing polynomial splines with adaptively selected and predictor-specific knots to fit the coefficients in varying coefficient models. An efficient dynamic programming algorithm is proposed to find the optimal solution. Numerical results show that the new method can achieve significantly smaller mean squared errors for coefficients compared with the equidistant spline fitting method.