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

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.

References in corpus (2)

• Extensions of smoothing via taut strings
• Data-driven wavelet-Fisz methodology for nonparametric function estimation

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