Returns of risky assets are often modelled as the product of a volatility function and standard Gaussian white noise. Long range data cannot be adequately approximated by simple parametric models. The choice is between retaining simple models and segmenting the data, or to use a non-parametric...

It is shown how to choose the smoothing parameter in image denoising by a statistical multiresolution criterion, both globally and locally. Using inhomogeneous diffusion and total variation regularization as examples for localized regularization schemes, an efficient method for locally adaptive...

A good robust functional should, if possible, be efficient at the model, smooth, and have a high breakdown point. M-estimators can be made efficient and Fréchet differentiable by choosing appropriate [psi]-functions but they have a breakdown point of at most 1/(p + 1) in p dimensions. On the...

The Neyman--Pearson Lemma introduced the concept of optimality into statistics. The derivation of optimal procedures has since dominated non-Bayesian mathematical statistics. This article criticizes the use of optimality as it operates only within a class of models whose adequacy is not...