# Guest lecture by Professor Lutz Dumbgen

Professor Dumbgen’s lecture on the Log-Concave Densities and Bi-Log-Concave Distribution Functions is held on Tuesday 22.10.2013, at 13:00-14:00, in the seminar room 469 Publicum.

In nonparametric curve estimation, shape-constraints are interesting alternatives to more traditional and often vague smoothness constraints. In particular, such constraints may lead to honest confidence regions which are valid for finite sample sizes. In this talk we present some recent results on two types of such constraints. The first and stronger constraint is that an underlying unknown probability density f is log-concave. We discuss some of its implications. The second and weaker constraint is that the underlying distribution function F is bi-log concave in the sense that both log(F) and log(1-F) are concave. It is shown that this constraint leads to rather accurate and honest confidence bands for F and, for instance, consistent confidence intervals for arbitrary moments of F.

# Guest lecture by Professor Lutz Dumbgen

Professor Dumbgen’s lecture on the Log-Concave Densities and Bi-Log-Concave Distribution Functions is held on Tuesday 22.10.2013, at 13:00-14:00, in the seminar room 469 Publicum.

In nonparametric curve estimation, shape-constraints are interesting alternatives to more traditional and often vague smoothness constraints. In particular, such constraints may lead to honest confidence regions which are valid for finite sample sizes. In this talk we present some recent results on two types of such constraints. The first and stronger constraint is that an underlying unknown probability density f is log-concave. We discuss some of its implications. The second and weaker constraint is that the underlying distribution function F is bi-log concave in the sense that both log(F) and log(1-F) are concave. It is shown that this constraint leads to rather accurate and honest confidence bands for F and, for instance, consistent confidence intervals for arbitrary moments of F.