Multiscale interpretation of taut string estimation and its connection to Unbalanced Haar wavelets
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.
KeywordsMultiscale Unbalanced Haar wavelets Taut string Nonparametric function estimation
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