Date/Time
Date(s) - 15/11/2022
3:30 pm - 5:00 pm

Title: Multivariate modelling using copulas with log-concave marginals

Speaker: Hanna Jankowski, York University

Abstract: Statistical modelling and inference using shape constraints, in particular log-concave densities, has received considerable and well-deserved attention over the past fifteen years. Density estimation via nonparametric likelihood is robust, yet requires no tuning parameters. In one dimension the rate of convergence is known to be $n^{?2/5}$, but slows down to at best $n^{?1/(d+1)}$ for higher dimensions (Doss and Wellner, 2016; Kim and Samworth, 2016). In order to obtain faster convergence in multivariate density estimation additional constraints are required. One option is to impose symmetry conditions, e.g. elliptical symmetry (Xu and Samworth, 2021). Copulas with log-concave marginals are another alternative, briefly considered by Chang and Walther (2007). Our goal is to study this latter approach in greater detail.  We establish a faster rate of convergence and study the finite sample performance using simulations in both the well- and miss-specified settings. 

This is joint work with Sawitree Boonpatcharanon from Chulalongkorn University.

Date/Time: Tuesday November 15, 2022, 3:30 – 5:00 

Location: UH 112