Séance du 22 octobre 2012

Lundi 22 octobre 2012

Organisateur: Karine Tribouley

Premier cours d'une série de trois cours. Les deux suivants ont lieu dans le cadre du séminaire "Point de Vue" du LMPA

14h00-16h Richard Nickl (University of Cambridge)

Titre : Confidence Sets in Sparse Regression

Résumé : The theory of statistical inference classically consists of the three key concepts: estimation - testing - confidence sets. In sparse high-dimensional linear models, or in nonparametric regression/density models, a remarkable breadth of adaptive \textit{estimation} results has been obtained in the last decade: particularly 'oracle inequalities', risk bounds and model selection consistency results. Unlike in classical parametric models, however, it is not straightforward to construct a confidence set in any of these models in a way that would be adaptive to the unknown sparsity or smoothness. A key aspect of statistical inference is, however, to be able to estimate the accuracy of adaptive estimation. In this series of three lectures I will try to discuss some recent results, both of a negative and positive kind, on how to make inference in such situations.