Séminaire SOP prévu le jeudi 14 novembre 2024 à 14h Amphi C06

Orateur : Stefano FORTUNATI

Title : Parametric, mismatched and semiparametric estimation: how to reconcile robustness and efficiency.

Abstract : In statistics, all the available knowledge about a phenomenon of interest is summarized in the probability density function (pdf) of the collected observations from a random experiment. To this end, we define a model as the family of pdfs that are able to statistically characterize the observations. The most used class of models are the parametric ones, in which the concept of efficiency is well defined by means of the Fisher Information Matrix. However, parametric models require the perfect match between the actual data distribution and the assumed model itself. Nevertheless, in practice, a certain amount of mismatch is often inevitable. Therefore, being aware about the possible efficiency loss that the derived estimator could undergone under model misspecification is of crucial importance. Even more important would be the possibility to overcome this misspecification. This can be achieved by adopting the more robust semiparametric models. Specifically, a semiparametric model is parameterized by a finite-dimensional parameter vector and by a possibly infinite-dimensional nuisance parameter that can be used to characterize the lack of knowledge in the functional form the data pdf. Deriving efficient (in a semiparametric sense) estimators of the finite dimensional vector may reconcile the two dichotomic concepts of robustness and efficiency. To fix the ideas, the set of elliptical distribution will be used as “fil rouge” to analyses the three above-mentioned aspects. 

The aim of this seminar is then to discuss i) the definition of statistical efficiency and ii) the possibility of deriving efficient estimators in parametric, misspecified and semi-parametric models. Finally, some (of the many) still open problems will be presented.