Research Interests
Research Interests
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Below are some topics I have worked on in the past. Full texts to most papers are linked under Publications.
Change-point analysis
Change-point analysis
We develop tools for detecting changes in certain characteristics of an observed time series, such as the mean (Vogel & Wendler 2017) or the variance (Gerstenberger, Vogel, Wendler 2020) or the cross-sectional dependence (Dehling, Vogel, Wendler, Wied 2017, Vogel & Fried 2015). Classical test for this purpose are based on estimates for the second moments. These are not very well suited for heavy-tailed data, which, in many areas of applications, are rather the norm than the exception. The common theme of our work is an improved efficiency under heavy tails (actually moment-free) - while retaining the same performance under normality. When studying alternatives the the classical methods, we observe interesting aspects, which can be used to devise more powerful change-point tests (Dehling, Vogel, Wendler 2026).
Graphical models
Graphical models
Graphical models provide a powerful tool to model complex systems with uncertainties. Conditional dependencies are represented by the edges of a graph, and graph-theoretic methods are employed in their analysis. The traditional working assumption is multivariate normality, which leads to the term “Gaussian graphical models” and allows a statistical inference based on the maximum-likelihood paradigm. We extended this to the semi-parametric class of elliptical distributions and show that graphical modelling can be based upon any covariance matrix estimator - as long as it satisfies two natural conditions: asymptotic normality and affine equivariance (Vogel & Fried 2011). We also propose Graphical M-estimators (Vogel & Tyler 2014) for robustly fitting graphical models. These work also for n < p.
Music performance anxiety (MPA)
Music performance anxiety (MPA)
We investigate the origins of music performance anxiety, e. g., how it is related to childhood experiences (Wiedemann, Vogel, Voss, Nusseck, Hoyer 2020) and other types of anxieties (Wiedemann, Vogel, Voss, Hoyer 2021). This is fundamental research aimed at finding effective therapies for MPA. And it is a nice application of a variaty of methods of multivariate statistics - graphical models being one of them.
Scale measures
Scale measures
Gini's mean difference derives its name from its appearance in a 1912 paper by Corrado Gini. It is the enumerator of the Gini ratio and as such often used, but as scale measure it has led much of a wallflower life in statistics. Maybe unfairly so: we show that it has very good statistical properties (Gerstenberger & Vogel 2015). The distance standard deviation is another scale measure, which is related to the much acclaimed distance correlation. (Edelmann, Richards, Vogel 2020).
Robust high-dimensional correlation estimation
Robust high-dimensional correlation estimation
The sample Pearson correlation matrix has a variety of very good statistical properties, among them: (1) it is guaranteed to be non-negative definite, (2) it is very fast to compute, and (3) it can be computed if n < p, i.e., if the number of variables exceeds the number of observations. However, it has one disadvantage: it does note cope well with heavy-tailed data. Alternative correlation matrix estimators that overcome that drawback usually fail at least one of the above three. Dürre, Fried, Vogel 2017 describe a correlation matrix estimator that is very robust with respect to heay tails (and defined without any moment assumption) and possesses the three desirable properties above. This work is based on a series of earlier papers that lay the foundations: Dürre, Vogel, Tyler 2014; Dürre, Vogel, Fried 2015; Dürre, Vogel 2016; Dürre, Tyler, Vogel 2016.
The effect of the COVID pandemic on ADHD medication prescriptions worldwid
The effect of the COVID pandemic on ADHD medication prescriptions worldwid
As with many things the COVID pandemic also disrupted the ADHD medication sales, but how? When we compare the numbers for 2019 and 2020, we find they are very similar, within a 1% margin of each other (Gimbach et al. 2023). So, no impact at all? Of course not, ADHD sales worldwide had seen a rise in the years prior to 2020, which was expected to continue in 2020. When we compare the actual sales in 2020 to their forecast based on the years 2014-2019, we observe a 6% drop (unweighted average per country). However, toward the end of 2021, the ADHD medication sales increase accelerates again, exceeding pre-pandemic levels. Do we observe a catch-up effect of the dip in 2020 or persisting trend change? We answer this question based on data until the end of 2022 (Gimbach et al. 2024).
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