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

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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.

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Authors and Affiliations

  1. Department of Statistics, Columbia House, London School of Economics, Houghton Street, London, WC2A 2AE, UK

    Haeran Cho & Piotr Fryzlewicz

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  1. Haeran Cho
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  2. Piotr Fryzlewicz
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Correspondence to Haeran Cho.

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Cho, H., Fryzlewicz, P. Multiscale interpretation of taut string estimation and its connection to Unbalanced Haar wavelets. Stat Comput 21, 671–681 (2011). https://doi.org/10.1007/s11222-010-9200-5

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