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Lundi 3 avril 2017

IntervenantAngelika ROHDE (Université de Freiburg)


"Locally adaptive confidence bands"


De 15h à 16h15, en salle 08 à l'ENSAE : 3 avenue Pierre Larousse à Malakoff (Tram T3: "Porte de Vanves" ou Métro 13 : "Porte de Vanves" ou "Malakoff Plateau de Vanves")

 

 

We develop honest and locally adaptive confidence bands for probability densities. They provide substantially improved confidence statements in case of inhomogeneous smoothness, and are easily implemented and visualized. The article contributes conceptual work on locally adaptive inference as a straightforward modification of the global setting imposes severe obstacles for statistical purposes. Among others, we introduce a statistical notion of local H\"older regularity and prove a correspondingly strong version of local adaptivity. We substantially relax the straightforward localization of the self-similarity condition in order not to rule out prototypical densities. The set of densities permanently excluded from the consideration is shown to be pathological in a mathematically rigorous sense. On a technical level, the crucial component for the verification of honesty is the identification of an asymptotically least favorable stationary case by means of Slepian's comparison inequality. This is a joint work with Tim Patschkowski. 

 

Ce séminaire est organisé par :

Alexandre TSYBAKOV         (Laboratoire de Statistique-CREST)

 

Cristina BUTUCEA                (Laboratoire de Statistique-CREST)