Inference on covariance operators via concentration inequalities

Inference on covariance operators is an important part of functional data analysis. Panaretos, Kraus, and Maddocks (2010) compare covariance operators for Gaussian process data. Pigoli, Aston, Dryden, and Secch. (2014) consider a variety of metrics over the space of covariance operators. In this talk, we propose a novel approach to the analysis of covariance operators making use of concentration inequalities. First, non-asymptotic confidence sets are constructed for such operators. Then, subsequent applications including a k sample test for equality of covariance, a functional data classifier, and an expectation-maximization style clustering algorithm are derived and tested on both simulated and phoneme data. contact: piercesare.secchi@polimi.it