Inference on covariance operators via concentration inequalities:   k-sample tests, classification, and clustering via Rademacher complexities
  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. 
Adam B. Kashlak, John A. D. Aston, Richard Nickl
stat.ME math.ST stat.TH