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.