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

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  • Adam B. Kashlak

    (University of Cambridge
    University of Alberta)

  • John A. D. Aston

    (University of Cambridge)

  • Richard Nickl

    (University of Cambridge)

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.

Suggested Citation

  • Adam B. Kashlak & John A. D. Aston & Richard Nickl, 2019. "Inference on Covariance Operators via Concentration Inequalities: k-sample Tests, Classification, and Clustering via Rademacher Complexities," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 214-243, February.
    • Handle: RePEc:spr:sankha:v:81:y:2019:i:1:d:10.1007_s13171-018-0143-9
    DOI: 10.1007/s13171-018-0143-9
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    References listed on IDEAS

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