Sankhya: The Indian Journal of Statistics

2007, Volume 69, Pt. 1, 1--27

Estimation of Piecewise-smooth Functions by Amalgamated Bridge Regression Splines

Felix Abramovich, Tel Aviv University, Israel
Anestis Antoniadis, University Joseph Fourier, France
Marianna Pensky, University of Central Florida, USA

SUMMARY. 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.

Key words and phrases. Amalgamation, bridge regression, jumps detection, nonparametric regression, penalized regression splines, wavelets.

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