Low?rank approximation for smoothing spline via eigensystem truncation

Smoothing splines provide a powerful and flexible means for nonparametric estimation inference. With cubic time complexity, fitting smoothing spline models to large data is computationally prohibitive. In this paper, we use the theoretical optimal eigenspace derive low-rank approximation of estimates. We develop method approximate eigensystem when it unknown error bounds The proposed methods are easy implement with existing software. Extensive simulations show that new accurate, fast compare favourably against methods.