Local roughness penalties for regression splines (Q1855623)

A new nonparametric estimator of regression based on B-splines that can be adapted to locally varying signals through local roughness penalties is proposed. The asymptotic properties of this estimator are studied and the upper bounds for integrated square errors are briefly given both for deterministic and random designs. The proposed estimator has the optimal rate of convergence under the classical assumptions. Its good performance is confirmed by a simulation study via comparison with the estimator proposed by \textit{D. Ruppert} and \textit{R.J. Carroll} [Aust. N. Z. J. Stat. 42, 205-223 (2000)].