Sparse M-estimators in semi-parametric copula models

Speaker: Dr Benjamin Poignard

Affiliation: Osaka University

Online via Zoom: https://uqz.zoom.us/j/86088033106

Abstract

We study the large sample properties of sparse M-estimators in the presence of pseudo-observations. Our framework covers a broad class of semi-parametric copula models, for which the marginal distributions are unknown and replaced by their empirical counterparts. It is well known that the latter modification significantly alters the limiting laws compared to usual M-estimation. We establish the consistency and the asymptotic normality of our sparse penalized M-estimator, and we prove the asymptotic oracle property with pseudoobservations, including the case when the number of parameters is diverging. Our framework allows us to manage copula-based loss functions that are potentially unbounded. As additional results, we state the weak limit of multivariate rank statistics and the weak convergence of the empirical copula process indexed by such maps. We apply our inference method to the sparse estimation of the covariance matrix for Gaussian copulas and to the sparse estimation of conditional copula models. This is a joint work with Jean-David Fermanian (ENSAE-CREST).

About the presenter's meeting 

Dr Poignard is willing to have (30-min) 1-to-1 meeting with our colleagues and graduate students on the seminar day. Anyone who wants to schedule a meeting with him can contact Dr Mohamad Khaled to book a time slot.