Singularity estimation via structural intensity: applications and modifications

J. Campbell

Journal of Nonparametric Statistics, 2009, vol. 21, issue 1, 67-84

Abstract: The problem of determining the number and location of singularities in a nonparametric setting is of significant practical and theoretical importance. In this paper, we examine an interesting new technique, the so-called strucural intensity of the wavelet modulus maxima that was recently suggested by Bigot [J. Bigot, A scale-space approach with wavelets to singularity estimation, ESAIM Probab. Statist. 9 (2005), pp. 143–164 (electronic)]. In doing so, an upper bound on the asymptotic rate of convergence for the associated estimator is determined and appropriate modifications are suggested where the empirical estimation technique is found to be inappropriate or otherwise simply left undefined. These clarifications should enable this promising tool to be employed with more confidence in future applications.

Date: 2009
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DOI: 10.1080/10485250802449755

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