El Departamento de Matemáticas y Estadística de la Universidad Torcuato Di Tella invita a la charla sobre How to estimate a density on a spider web?, a cargo de Dominique Picard (CNRS, Université Pierre et Marie Curie).


Abstract

Our purpose  is to study the density estimation problem, namely, one observes X_1,...,X_n that are i.i.d. random variables defined on a space M and the problem is to find a good estimation to the common density function. This problem has a long history in mathematical statistics but here we will consider very general sets M such as Riemannian manifolds or sets of matrices or  graphs or spider webs and prove that with some assumptions, we can build an estimation theory with estimation procedures, regularity sets and upper bounds evaluations quite parallel to what has been neatly done in R^d.

In particular we prove that kernel methods can be constructed with minimax and oracle properties. If we want to roughly summarize the basic assumptions that will be made in this work, let us mention that some of them are concerning the basic dimensional structure of the set (doubling conditions...), whereas others are devoted to construct an environment where regularity spaces and approximation properties hold. This setting is quite general but at the same time is sufficiently rich in allowing the development of a smooth functional calculus with well localized spectral kernels, Besov regularity spaces, and wavelet type systems. 

Naturally, the classical setting on R^d and the one on the sphere are contained in this general framework, but also various other settings are covered. In particular, spaces of matrices, of graphs, of compact Riemannian manifolds, convex subsets of (non-compact) Riemannian manifolds are covered.

La charla se realizará en inglés sin traducción.