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Functional Statistics and Related Fields pp 279–286Cite as

Random Functional Variable and Fourier Series

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Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

Abstract

This paper presents how a functional random variable can be expressed in the form of Fourier series. This expansion can be used for the definition of components of the functional random variable and for the approximation of the random curves as the partial sum of the Fourier series. Thus we can estimate the distribution of the components, simulate the functional random variable with given components and compute some characteristics of the distribution of its norm.

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References

  1. Ferraty, F. ed.:Recent Advances in Functional Data Analysis and Related Topics. Springer Science & Business Media (2011)

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  2. Ferraty, F., Vieu, P.: Nonparametric Functional Data Analysis: Theory and Practice. Springer Series in Statistics, Springer, New York (2006)

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  3. NPFDA web page: https://www.math.univ-toulouse.fr/staph/npfda/

  4. Rachdi, M., Vieu P.: Nonparametric regression for functional data: Automatic smoothing parameter selection. J. Statist. Plann. Inference 137(9), 2784-2801, (2007)

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  5. Rudin, W.: Real and Complex Analysis. McGraw Hill (1970)

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  6. Ushakov, N.G.: Selected Topics in Characteristic Functions, De Gruyter (1999)

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlářská 2, Brno, Czech Republic

    Jiří Zelinka

Authors
  1. Jiří Zelinka
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Correspondence to Jiří Zelinka .

Editor information

Editors and Affiliations

  1. Dept. of Mathematics, University of A Coruña, A Coruña, Spain

    Germán Aneiros

  2. Dept. of Studies in Econ.and Business, University of Eastern Piedmont "Amedeo Avogadro", Novara, Italy

    Enea G. Bongiorno

  3. Dept. of Mathematics, University of A Coruña, A Coruña, Spain

    Ricardo Cao

  4. Toulouse Mathematics Institute (IMT), Paul Sabatier University, Toulouse, France

    Philippe Vieu

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Zelinka, J. (2017). Random Functional Variable and Fourier Series. In: Aneiros, G., G. Bongiorno, E., Cao, R., Vieu, P. (eds) Functional Statistics and Related Fields. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-55846-2_36

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