Webinar: Some Unexplored Connections between Measure Transportation Theory and Statistical Inference

To participate, please send an email to: eb-secr@ese.eur.nl

Measure transportation theory is a growing field of mathematics and it is popular in many other disciplines.

For instance, optimal transportation mappings (related to the results of Monge & Kantorovich) are widely-applied in bioengineering (e.g. for image analysis), in economics (e.g. for resources allocation), in physics (e.g. for fluids dynamics analysis), in machine learning (e.g. for classification), just to name a few. In this talk, I unveil some unexplored links between Monge & Kantorovich results and statistical inference. The talk consists in two parts. First, I explain how the solution to the Kantorovich dual problem can be applied to derive small sample asymptotics, as obtained using saddlepoint techniques for M-estimators. I will briefly present some new results in time series and in spatial econometrics. The key aspect of the whole construction is the derivation of the saddlepoint density approximation via the method of the conjugate density. The derivation hinges on convex analysis results and it makes use of the notion of Legendre transform. Second, I explain how the solution to the Kantorovich primal problem can be applied to derive a novel class of semiparametric R-estimators for VARMA models. The proposed R-estimators hinge on novel concepts of ranks and signs, as obtained from measure transportation arguments, which allow to overcome the clas-sical problem of lack of canonical order in Rd, d ≥ 2. Numerical results illustrate the findings of the two parts of the talk.