Title: Robust sieve M-estimation with an application to dimension reduction
Authors: Julien Bodelet - University of Geneva (Switzerland) [presenting]
Davide La Vecchia - University of Geneva (Switzerland)
Abstract: Non/semiparametric techniques are routinely applied in the analysis of high dimensional data. Robust procedures for such techniques are highly requested, since the huge amount of records can make outlier detection very difficult. We explain how to achieve robust dimension reduction using sieve M-estimators, which represent a general and flexible class of estimators for non/semiparametric models. First, by means of the von Mises calculus for statistical functionals and the empirical process theory, a new theoretical device, called sieve Influence Function, suitable to characterize the class of infinitesimally robust sieve M-estimators, is introduced. Then, rates of convergence of the robust estimators on non-convex sieve spaces are derived: this extends the asymptotic results available for sieve M-estimators on convex sieve spaces. Finally, the use of the estimation procedure is illustrated for the class of Dynamic Semiparametric Factor Models, which are applied for dimension reduction in the analysis of functional Magnetic Resonance Imaging (fMRI) data. Monte Carlo simulations illustrate that the robust M-estimators outperform classical sieve M-estimators in the presence of outliers. An application to real fMRI data is also shown.