Advertisement

Random Functional Variable and Fourier Series

Conference paper
Part of the Contributions to Statistics book series (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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ferraty, F. ed.:Recent Advances in Functional Data Analysis and Related Topics. Springer Science & Business Media (2011)Google Scholar
  2. 2.
    Ferraty, F., Vieu, P.: Nonparametric Functional Data Analysis: Theory and Practice. Springer Series in Statistics, Springer, New York (2006)Google Scholar
  3. 3.
  4. 4.
    Rachdi, M., Vieu P.: Nonparametric regression for functional data: Automatic smoothing parameter selection. J. Statist. Plann. Inference 137(9), 2784-2801, (2007)Google Scholar
  5. 5.
    Rudin, W.: Real and Complex Analysis. McGraw Hill (1970)Google Scholar
  6. 6.
    Ushakov, N.G.: Selected Topics in Characteristic Functions, De Gruyter (1999)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Mathematics and Statistics, Faculty of ScienceMasaryk UniversityBrnoCzech Republic

Personalised recommendations