Zuzana Hübnerová

EEG, Nonparametric Multivariate Statistics, and Dementia Classification

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.

Properties of some test of equality of two negative binomial samples

When comparing two independent samples from the negative binomial distribution the test of equality of their expected values might be of interest. In this case, the assumptions on the nuisance shape parameter determine the form of suitable test statistic. This paper focuses on test based on Wald statistic under an assumption that the shape parameters in the two samples are known and equal. However, the common shape parameter might be replaced by its estimate, either statistical or expert. We discuss the consequences of this procedure on the power as well as on the size of the test (probability of rejection of H0 when it is true).