OPSTAT: Measure-characterising linear OPerators with applications to asymptotic analysis and STATistical inference

This project’s goal is to develop tools that can estimate the ‘dissimilarity’ between various probability distributions.

This type of problem occurs in particular in the context of applications of the well-known central limit theorem, the idea being to replace an empirical distribution (which is intrinsically complex and difficult to manipulate) with a normal distribution (which is intrinsically simple and easy to apply).

The researchers’ work will consist in developing estimators that can quantify the impact of such a substitution on later decisions, not only within a Gaussian framework, but also when comparing any two probability distributions.

From a methodological standpoint, the main tool developed is a series of integro-differential operators known as ‘Stein operators’, which can characterize any probability distribution using tools with solid theoretical and numerical properties.

Coordination: Yvik Swan, Unité de recherche en Statistique mathématique et Probabilités, Faculté des Sciences

 

Dates
Created on September 4, 2020