From Unbalanced and Shape-Adaptive Wavelets to Wild Binary Segmentation

• Activity Number: 227
• Type: Topic Contributed
• Date/Time: Monday, August 5, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Piotr Fryzlewicz*+
• Companies: London School of Economics
• Keywords: wavelets ; change-point detection ; nonparametric regression ; image smoothing ; adaptivity ; binary segmentation

Abstract

The use of wavelets in nonparametric regression problems is often blighted by unwanted artefacts, poor performance in highly noisy settings and difficulties in interpreting the outcome. In this talk, we argue that these issues can to a large extent be remedied by the use of "adaptive wavelets", i.e. wavelets with data-dependent shapes. We provide an overview of our recent work in this area using the examples of Unbalanced Haar wavelets in curve estimation, SHape-Adaptive Haar (SHAH) wavelets in image denoising, as well as the Wild Binary Segmentation method for multiple change-point detection in curves, which has an Unbalanced Haar wavelet interpretation.