The 1995 wavelet paper of Donoho, Johnstone, Kerkyacharian and Picard

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• Richard Nickl, University of Cambridge
• Wednesday 26 November 2008, 16:30-17:30
• MR11, CMS.

If you have a question about this talk, please contact Richard Samworth.

The minimax paradigm in statistical function estimation is a quite flexible but also complicated way to assess the performance of statistical estimation procedures in cases where the parameter space is infinite-dimensional. It usually consists of

a) an observational model, e.g., regression, density, white noise, etc.; b) a prescribed infinite-dimensional parameter space over which one wants to have a uniformly optimal procedure; c) a loss function on the parameter space that measures closeness and hence ‘optimality’

In discussing the paper, we will first see that all permutations of possible choices in a)-c) lead to a quite confusing (but not meaningless) complexity, which basically poses two main statistical challenges: ‘Spatial Adaptation’ and ‘Adaptation to unknown smoothness’.

The main discussion of the paper will then focus on the remarkable fact that the authors provided a universal, simple and computable ‘nearly optimal’ simultaneous solution to all these problems by means of a ‘wavelet shrinkage’ estimation procedure, that I will try to explain in some detail, including a quick crash course in wavelets.

The link to the paper, with discussion, is here

http://www.jstor.org/stable/pdfplus/2345967.pdf

This talk is part of the Statistics Reading Group series.

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