We construct a testing procedure for monotonicity on some interval in the statistical models of density deconvolution and signal deblurring under white noise. The corresponding error probabilities are studied with particular attention to their asymptotic properties.

We derive the optimal convergence rates for density estimation based on aggregated observations under common smoothness conditions for symmetric densities. We study a procedure for data-driven bandwidth selection and give an extension to skew densities.

We consider the problem of estimating the support of a multivariate density based on contaminated data. We introduce an estimator, which achieves consistency under weak conditions on the target density and its support, respecting the assumption of a known error density. Especially, no smoothness...