Change Point Detection Using Penalized Multidegree Splines

We consider a function estimation method with change point detection using truncated power spline basis and elastic-net-type L 1 -norm penalty. The L 1 -norm penalty controls the jump detection and smoothness depending on the value of the parameter. In terms of the proposed estimators, we introduce two computational algorithms for the Lagrangian dual problem (coordinate descent algorithm) and constrained convex optimization problem (an algorithm based on quadratic programming). Subsequently, we investigate the relationship between the two algorithms and compare them. Using both simulation and real data analysis, numerical studies are conducted to validate the performance of the proposed method.