Multiscale quantile regression

We introduce a new methodology for analyzing serial data by quantile regression assuming that the underlying quantile function consists of constant segments. The procedure does not rely on any distributional assumption besides serial independence. It is based on a multiscale statistic, which allows to control the (finite sample) probability for selecting the correct number of Read more…

Multiscale blind source separation

We provide a new methodology for statistical recovery of single linear mixtures of piecewise constant signals (sources) with unknown mixing weights and change points in a multiscale fashion. We show exact recovery within an ε-neighborhood of the mixture when the sources take only values in a known finite alphabet. Based on this we provide the Read more…

Minimax estimation in linear models with unknown finite alphabet design

We provide minimax theory for joint estimation of F and ω in linear models Y=Fω+Z where the parameter matrix ω and the design matrix F are unknown but the latter takes values in a known finite set. This allows to separate F and ω, a task which is not doable, in general. We obtain in Read more…

Identifiability for blind source separation of multiple finite alphabet linear mixtures

We give under weak assumptions a complete combinatorial characterization of identifiability for linear mixtures of finite alphabet sources, with unknown mixing weights and unknown source signals, but known alphabet. This is based on a detailed treatment of the case of a single linear mixture. Notably, our identifiability analysis applies also to the case of unknown Read more…