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. keywords: multiscale, Unbalanced Haar wavelets, taut string, nonparametric function estimation. ∗Department of Statistics, Columbia House, London School of Economics, Houghton Street, London, WC2A 2AE, UK. E-mail: [email protected], [email protected]