Title: Inference on Covariance Operators via Concentration Inequalities: k-sample Tests, Classification, and Clustering via Rademacher Complexities

Author(s): Adam B. Kashlak, Adam B. Kashlak, John A. D. Aston and Richard Nickl
Issue: Volume 81 Series A Part 1 Year 2019
Pages: 214 -- 243
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.
Primary 62G05; Secondary 62G15.
Keywords and phrases: Functional data analysis, Manifold data, Non-asymptotic confidence sets, Concentration of measure.