Lévy Adaptive B-spline Regression via Overcomplete Systems

The estimation of functions with varying degrees smoothness is a challenging problem in the nonparametric function estimation. In this paper, we propose LABS (L\'{e}vy Adaptive B-Spline regression) model, an extension LARK models, for smoothness. model B-spline bases as generating kernels. basis consists piecewise k degree polynomials k-1 continuous derivatives and can express systematically By changing orders basis, adapt functions, i.e., jump discontinuities, sharp peaks, etc. Results simulation studies real data examples support that catches not only smooth areas but also jumps peaks functions. proposed has best performance almost all examples. Finally, provide theoretical results mean belongs to certain Besov spaces based on prior full spaces.