Séance du 31 mai 2010

Lundi 31 mai 2010 Amphi Darboux

Organisateurs: Marc Hoffmann et Karine Tribouley

14h00 Alain Pajor (Université de Marne la Vallée)

Approximation de la matrice de covariance d'un vecteur aléatoire

Résumé: On considère un vecteur aléatoire de dimension n. On s'intéresse à la question suivante: quelle doit-être la taille N d'un échantillon de même loi que X, pour que la matrice de covariance empirique soit une bonne approximation de la matrice de covariance de X.

15h00 Marianna Pensky (University of Central Florida)

Estimation of a Regression Function on the Basis of Incomplete Data

Abstract: Applicability of majority of techniques for estimation in nonparametric regression model rests on the assumption that data is equally spaced and complete. These assumptions were adopted by signal processing community where the signal is assumed to be recorded at equal intervals in time. However, in reality, due to unexpected loss of data or limitations of data sampling techniques, data may fail to comply with these assumptions. To this end, we consider a problem of recovering a function on the basis of irregularly spaced observations where the design density has a zero of a polynomial or exponential order. These two assumptions correspond to a moderate or severe data loss, respectively. The resulting problem turns out to be ill-posed.Under the assumption that the design density is known, we construct adaptive estimators for the regression function and derive lower and upper bounds for the risk.

16h00 Axel Munk (Université de Goetingen)

Statistical Multiscale Analysis: From Biomembranes to Biomolecular Microsopy

Abstract: In this talk we will discuss the concept of statistical multiscale analysis in order obtain fully data driven reconstructions from a given regularisation method. To this end, the extreme value behaviour of the residuals has to be studied. We discuss in detail a version of locally adaptive total variation penalization for statistical inverse problems and adress some computational issues. Our work is illustrated by several applications from biophyisics, e.g. from ion channel experiments of biomembranes and from nansocale biophotonics.