Jon A. Wellner will discuss the Maximum Likelihood Estimators (MLEs) of log-concave and s-concave densities on R and Rd, and review some of the properties of these estimators, both good and bad. He will also discuss recent results for the R enyi divergence estimators proposed by Koenker and Mizera (2010). (Based on joint work with Charles Doss, Qiyang (Roy) Han, and Arseni Seregin.)
This seminar will be based on the following 3 papers:
Approximation and estimation of s-concave densities via rényi divergences by Qiyang Han and Jon A Wellner
Nonparametric estimation of multivariate convex-transformed densities by Arseni Seregini and Jon A Wellner
Global rates of convergence of the mles of log-concave and s−concave densities by Charles R Doss and Jon A Wellner