The asymptotic behaviour of the minimax risk can be used as a measure of how 'hard' an estimation problem is. We relate the asymptotic behaviour of this quantity to an appropriate modulus of continuity, using elementary ideas and techniques only.

The standard isotonic regression of a vector in is the solution to a least squares projection problem on the cone of vectors with 'increasing components' in . Generalized isotonic regression problems are isotonic optimization problems that seem to be quite different from isotonic regression...

We consider deconvolution models with noise variables that have bounded, decreasing densities with compact support. The nonparametric maximum likelihood estimator of the distribution function is shown to converge globally at a rate n-1/3 with respect to theL2-metric.

Consider a stationary sequence of random variables with infinitely divisible marginal law, characterized by its Lévy density. We analyse the behaviour of a so-called cumulant M-estimator, in case this Lévy density is characterized by a Euclidean (finite dimensional) parameter. Under mild...

We consider estimation of the upper boundary point "F"-super- - 1 (1) of a distribution function "F" with finite upper boundary or 'frontier' in deconvolution problems, primarily focusing on deconvolution models where the noise density is decreasing on the positive halfline. Our estimates are...

In this paper, we study an algorithm (which we call the support reduction algorithm) that can be used to compute non-parametric "M"-estimators in mixture models. The algorithm is compared with natural competitors in the context of convex regression and the 'Aspect problem' in quantum physics....