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Exact tests for the means of Gaussian stochastic processes

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  • Ghiglietti, Andrea
  • Paganoni, Anna Maria

Abstract

This paper investigates the inferential properties of testing the means of Gaussian functional data, using a Mahalanobis type distance for Hilbert spaces. We establish the analytic power of exact and asymptotic tests, for the known and unknown covariance case, respectively.

Suggested Citation

  • Ghiglietti, Andrea & Paganoni, Anna Maria, 2017. "Exact tests for the means of Gaussian stochastic processes," Statistics & Probability Letters, Elsevier, vol. 131(C), pages 102-107.
    • Handle: RePEc:eee:stapro:v:131:y:2017:i:c:p:102-107
    DOI: 10.1016/j.spl.2017.08.001
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    References listed on IDEAS

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    1. Duchesne, Pierre & Lafaye De Micheaux, Pierre, 2010. "Computing the distribution of quadratic forms: Further comparisons between the Liu-Tang-Zhang approximation and exact methods," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 858-862, April.
    2. 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.
    3. 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.
    4. Cuevas, Antonio & Febrero, Manuel & Fraiman, Ricardo, 2006. "On the use of the bootstrap for estimating functions with functional data," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1063-1074, November.
    5. Florentina Bunea & Andrada E. Ivanescu & Marten H. Wegkamp, 2011. "Adaptive inference for the mean of a Gaussian process in functional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(4), pages 531-538, September.
    6. Guanqun Cao & Lijian Yang & David Todem, 2012. "Simultaneous inference for the mean function based on dense functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(2), pages 359-377.
    7. Joseph, Esdras & Galeano San Miguel, Pedro & Lillo Rodríguez, Rosa Elvira, 2013. "The Mahalanobis distance for functional data with applications to classification," DES - Working Papers. Statistics and Econometrics. WS ws131312, Universidad Carlos III de Madrid. Departamento de Estadística.
    8. 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.
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    Cited by:

    1. Liebl, Dominik & Walders, Fabian, 2019. "Parameter regimes in partial functional panel regression," Econometrics and Statistics, Elsevier, vol. 11(C), pages 105-115.
    2. Andrea Martino & Andrea Ghiglietti & Francesca Ieva & Anna Maria Paganoni, 2019. "A k-means procedure based on a Mahalanobis type distance for clustering multivariate functional data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(2), pages 301-322, June.

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    More about this item

    Keywords

    Functional data; Inference on the mean; Power of exact tests; Gaussian processes; Distances in L2;
    All these keywords.

    JEL classification:

    • L2 - Industrial Organization - - Firm Objectives, Organization, and Behavior

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