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