  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.
