Log-Concave Distributions in Nonparametric Density Estimation and Regression

Abstract

Log-concave distributions are an interesting and well-behaved nonparametric model. In the first part of the talk we present some fundamental properties of this model and discuss maximum-likelihood estimation based on i.i.d. data. In the second part we discuss potential applications to regression problems. The talk is based on joint work with Kaspar Rufibach, André Hüsler, Dominic Schuhmacher and Richard Samworth.