Title
Estimation Of Piecewise-Smooth Functions By Amalgamated Bridge Regression Splines
Keywords
Amalgamation; Bridge regression; Jumps detection; Nonparametric regression; Penalized regression splines; Wavelets
Abstract
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. © 2007, Indian Statistical Institute.
Publication Date
11-5-2007
Publication Title
Sankhya: The Indian Journal of Statistics
Volume
69
Issue
1
Number of Pages
1-27
Document Type
Article
Personal Identifier
scopus
Copyright Status
Unknown
Socpus ID
35649002468 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/35649002468
STARS Citation
Abramovich, Felix; Antoniadis, Anestis; and Pensky, Marianna, "Estimation Of Piecewise-Smooth Functions By Amalgamated Bridge Regression Splines" (2007). Scopus Export 2000s. 5887.
https://stars.library.ucf.edu/scopus2000/5887