Statistics and Computing

, Volume 21, Issue 4, pp 671–681

Multiscale interpretation of taut string estimation and its connection to Unbalanced Haar wavelets

Article

DOI: 10.1007/s11222-010-9200-5

Cite this article as:
Cho, H. & Fryzlewicz, P. Stat Comput (2011) 21: 671. doi:10.1007/s11222-010-9200-5

Abstract

We compare two state-of-the-art non-linear techniques for nonparametric function estimation via piecewise constant approximation: the taut string and the Unbalanced Haar methods. While it is well-known that the latter is multiscale, it is not obvious that the former can also be interpreted as multiscale. We provide a unified multiscale representation for both methods, which offers an insight into the relationship between them as well as suggesting lessons both methods can learn from each other.

Keywords

MultiscaleUnbalanced Haar waveletsTaut stringNonparametric function estimation

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Statistics, Columbia HouseLondon School of EconomicsLondonUK