Title: Estimation of Piecewise-smooth Functions by Amalgamated Bridge Regression Splines

Author(s): Felix Abramovich, Anestis Antoniadis and Marianna Pensky
Issue: Volume 69 Part 1 Year 2007
Pages: 1 -- 27
We consider nonparametric estimation of a one-dimensional piecewise-smooth function observed with white Gaussian noise on an interval. We propose a two-step estimation procedure, where one first detects jump points by a wavelet-based procedure and then estimates the function on each smooth segment separately by bridge regression splines. We prove the asymptotic optimality (in the minimax sense) of the resulting amalgamated bridge regression spline estimator and demonstrate its efficiency on simulated and real data examples.
AMS (2000) subject classification. Primary 62G05, 62G08; secondary 65D07.
Keywords and phrases: Amalgamation, bridge regression, jumps detection, nonparametric regression, penalized regression splines, wavelets.