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Quadratic forms of the empirical processes for the two-sample problem for functional data

Author

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  • R. Bárcenas

    (CIMAT)

  • J. Ortega

    (CIMAT)

  • A. J. Quiroz

    (Universidad de Los Andes)

Abstract

The use of quadratic forms of the empirical process for the two-sample problem in the context of functional data is considered. The convergence of the family of statistics proposed to a Chi-squared limit is established under metric entropy conditions for smooth functional data. The applicability of the proposed methodology is evaluated in simulations and real data examples.

Suggested Citation

  • R. Bárcenas & J. Ortega & A. J. Quiroz, 2017. "Quadratic forms of the empirical processes for the two-sample problem for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 503-526, September.
    • Handle: RePEc:spr:testjl:v:26:y:2017:i:3:d:10.1007_s11749-017-0522-x
    DOI: 10.1007/s11749-017-0522-x
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    References listed on IDEAS

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    1. 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.
    2. Mikosch, T., 1991. "Functional limit theorems for random quadratic forms," Stochastic Processes and their Applications, Elsevier, vol. 37(1), pages 81-98, February.
    3. André Mas, 2007. "Testing for the Mean of Random Curves: A Penalization Approach," Statistical Inference for Stochastic Processes, Springer, vol. 10(2), pages 147-163, July.
    4. Lajos Horváth & Piotr Kokoszka & Ron Reeder, 2013. "Estimation of the mean of functional time series and a two-sample problem," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(1), pages 103-122, January.
    5. Gina-Maria Pomann & Ana-Maria Staicu & Sujit Ghosh, 2016. "A two-sample distribution-free test for functional data with application to a diffusion tensor imaging study of multiple sclerosis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(3), pages 395-414, April.
    6. Fremdt, Stefan & Horváth, Lajos & Kokoszka, Piotr & Steinebach, Josef G., 2014. "Functional data analysis with increasing number of projections," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 313-332.
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    Cited by:

    1. Jiang, Qing & Hušková, Marie & Meintanis, Simos G. & Zhu, Lixing, 2019. "Asymptotics, finite-sample comparisons and applications for two-sample tests with functional data," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 202-220.
    2. M. D. Jiménez-Gamero & M. Cousido-Rocha & M. V. Alba-Fernández & F. Jiménez-Jiménez, 2022. "Testing the equality of a large number of populations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 1-21, March.
    3. González–Rodríguez, Gil & Colubi, Ana & González–Manteiga, Wenceslao & Febrero–Bande, Manuel, 2024. "A consistent test of equality of distributions for Hilbert-valued random elements," Journal of Multivariate Analysis, Elsevier, vol. 202(C).

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