Seminar Details

Seminar Details


Monday

Jan 4

3:30 pm

Estimation of Convex-Transformed Densities

Arseni Seregin

Seminar

University of Washington - Department of Statistics

A convex-transformed density is a quasi-concave (or a quasi-convex) density which is a composition of a fixed monotone transformation and a convex function. Many parametric and non-parametric families of densities can be included in a suitable family of convex-transformed densities: normal, gamma, beta, Gumbel and other log-concave densities, multivariate Pareto, Burr, Student Snedecor etc.

We will discuss the role of convexity in shape constrained density estimation then introduce classes of convex-transformed densities and present our results related to estimation of a convex-transformed density: structure, existence and consistency of the maximum likelihood estimator, and asymptotic minimax lower bounds for estimation.