EEG, Nonparametric Multivariate Statistics, and Dementia Classification

book chapter

en

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.

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 projection, Rank statistics

20.09.2018

Springer International Publishing

978-3-319-76034-6

Statistics and Simulation, IWS 8, Vienna, Austria, September 2015

243–257

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