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

Author

Listed:
  • 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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    1. Davide Pigoli & John A. D. Aston & Ian L. Dryden & Piercesare Secchi, 2014. "Distances and inference for covariance operators," Biometrika, Biometrika Trust, vol. 101(2), pages 409-422.
    2. Stefan Fremdt & Josef G. Steinebach & Lajos Horváth & Piotr Kokoszka, 2013. "Testing the Equality of Covariance Operators in Functional Samples," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(1), pages 138-152, March.
    3. Ci-Ren Jiang & John A. D. Aston & Jane-Ling Wang, 2016. "A Functional Approach to Deconvolve Dynamic Neuroimaging Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 1-13, March.
    4. C. Abraham & P. A. Cornillon & E. Matzner‐Løber & N. Molinari, 2003. "Unsupervised Curve Clustering using B‐Splines," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(3), pages 581-595, September.
    5. Aurore Delaigle & Peter Hall, 2012. "Achieving near perfect classification for functional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(2), pages 267-286, March.
    6. Panaretos, Victor M. & Kraus, David & Maddocks, John H., 2010. "Second-Order Comparison of Gaussian Random Functions and the Geometry of DNA Minicircles," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 670-682.
    7. Chung Chang & Yakuan Chen & R. Ogden, 2014. "Functional data classification: a wavelet approach," Computational Statistics, Springer, vol. 29(6), pages 1497-1513, December.
    8. Ferraty, F. & Vieu, P., 2003. "Curves discrimination: a nonparametric functional approach," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 161-173, October.
    9. Peter L. Bartlett & Stéphane Boucheron & Gábor Lugosi, 2000. "Model selection and error estimation," Economics Working Papers 508, Department of Economics and Business, Universitat Pompeu Fabra.
    10. Gareth M. James & Trevor J. Hastie, 2001. "Functional linear discriminant analysis for irregularly sampled curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 533-550.
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