Cours CREST GENES - Cours de Formation Pour La Recherche



Cours CREST GENES - Cours de Formation Pour La Recherche - 2011 Uniform Probability Inequalities with Application in High-dimensional Statistical Models à l’ENSAE 3, Avenue Pierre Larousse, Malakoff (Métro : Malakoff/Plateau de Vanves)



Sara van de GEER (Seminar for Statistics, ETH, Zurich, et Invitée CREST, LS) We review some uniform probability and moment inequalities for sums of independent random variables indexed by a parameter. Concentration inequalities for three types of situations will be discussed: the case of sub-exponential, of sub- Gaussian, and of bounded random variables. As an elaborated example, we study the case where the parameter space is the convex hull of a set with small covering number, extending some entropy results of Ball and Pajor (1990). The results will be applied in high-dimensional statistical problems, where regularization is employed. One of our focus points here will be dealing with situations with highly correlated design. We moreover discuss high-dimensional nonlinear models. Most of the results will be presented with a full proof. The course aims at providing insight into the main ideas and a background for further development of the theory for high-dimensional statistical models. Cours Lundi 7 Mars 2011 De 14h à 16h 10 Amphi 2 Jeudi 10 Mars 2011 De 14h à 17h 15 Amphi 2



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