Inference on covariance operators via concentration inequalities: k-sample tests, classification, and clustering via Rademacher complexities

Abstract

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.

15 pages, 2 figures, 6 tables

References in corpus (3)

• Confidence bands in density estimation
• Distance-based clustering of sparsely observed stochastic processes, with applications to online auctions
• Global uniform risk bounds for wavelet deconvolution estimators

Cited by in corpus (3)

• Permutation tests for the equality of covariance operators of functional data with applications to evolutionary biology
• Improved Rademacher symmetrization through a Wasserstein based measure of asymmetry
• Covariance Operator Estimation via Adaptive Thresholding