On June, 19th to June, 21th 2018 we have the pleasure to welcome Céline DUVAL (Université Paris Descartes) with us. Céline will give a talk (see details below) in the Kolloquium für Statistik on Thursday, June 21th 2018. Do not hesitate to pass by her office (Room 4.412, MΛTHEMΛTIKON, INF 205) for a discussion.

Talk:

Kolloquium für Statistik

Thursday, June 21th 2018 14:00 c.t.

SR7, MΛTHEMΛTIKON, INF 205

Presented by:

Céline DUVAL (Université Paris Descartes)

Title:

Nonparametric adaptive estimator for grouped data and some generalizations

Abstract:

Suppose one wants to estimate the density of a random variable X from grouped data, i.e., when one only observes the sum of K ≥ 2 independent copies of X. This model is a building block to understand a wider inverse problem; nonparametric estimation of the jump density of a discretely observed jump process. In the grouped data context, we provide a constructive estimator based on a suitable definition of the logarithm of the empirical characteristic function and propose a new strategy for the data driven choice of the cut-off parameter. The adaptive estimator is proven to be minimax-optimal up to some logarithmic loss. Moreover, we discuss the fact that the definition of the adaptive estimator applies in a wider context than the one considered here. (Joint work with J. Kappus)