EEG, Nonparametric Multivariate Statistics, and Dementia Classification

  • Patrick Langthaler
  • Yvonne Höller
  • Zuzana Hübnerová
  • Vítězslav Veselý
  • Arne C. Bathke
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 231)


We are considering the problem of performing statistical inference with functions as independent or dependent variables. Specifically, we will work with the spectral density curves of electroencephalographic (EEG) measurements. These represent the distribution of the energy in the brain on different frequencies and therefore provide important information on the electric activity of the brain. We have data of 315 patients with various forms of dementia. For each individual patient, we have one measurement on each of 17 EEG channels. We will look at three different methods to reduce the high dimensionality of the observed functions: 1. Modeling the functions as linear combinations of parametric functions, 2. The method of relative power (i.e., integration over prespecified intervals, e.g., the classical frequency bands), and 3. A method using random projections. The quantities that these methods return can then be analyzed using multivariate inference, for example, using the R package npmv (Ellis et al., J Stat Softw 76(1): 1–18, 2017, [4]). We include a simulation study comparing the first two methods with each other and consider the advantages and shortcomings of each method. We conclude with a short summary of when which method may be used.


Dimension reduction Functional data Multivariate inference Random projections Rank statistics 



The chapter was finished during a research stay of the third author at the University of Warsaw supported by the grant of the Czech Ministry of Education, Youth and Sports.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Patrick Langthaler
    • 1
    • 2
  • Yvonne Höller
    • 2
    • 3
  • Zuzana Hübnerová
    • 4
  • Vítězslav Veselý
    • 4
  • Arne C. Bathke
    • 1
  1. 1.Paris-Lodron-University SalzburgSalzburgAustria
  2. 2.Paracelsus Medical University SalzburgSalzburgAustria
  3. 3.Department of Neurology, Christian Doppler Medical Centre and Centre of Cognitive NeuroscienceParacelsus Medical University SalzburgSalzburgAustria
  4. 4.Brno University of TechnologyBrnoCzech Republic

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