Robust sieve M-estimation with an application to dimensionality reduction

Abstract

We propose a sieve M-estimation procedure which combines the flexibility of semiparametric inference with the stability and reliability of infinitesimal robustness. We derive the asymptotic theory of the proposed estimators, studying their convergence rate. In the context of functional magnetic resonance imaging (fMRI) data analysis, we illustrate how to apply our procedure to conduct inference on a semiparametric dynamic factor model. Monte Carlo simulations and real data analysis exemplify the stability of our estimators, providing a comparison with the extant, non robust and routinely applied sieve M-estimators.