**(NMST611) Advanced Statistical Seminar 2024**

**Wednesday: 15:40 - 17:20**| Prezenčne v Praktiku KPMS

The advanced statistical seminar consists of presentations delivered (typically in person) by invited foreign speakers or departmental guests. Assorted topics from modern statistics -- theory and applications -- are usually communicated during the talks.

**Seminar schedule (Summer term 2024)**

**21.02.2024 | 15:40 | Ivan Mizera**

*University of Alberta, Canada*

**Title: Variations on Quantile Regression (in an Era of Machine Intelligence)***Various aspects and some applications of quantile regression are presented; in particular, partial quantile regression, a method of basis selection for functional linear quantile regression model, akin to partial least squares, is covered in some detail. Some perspectives for distributional regression fitting, with particular emphasis on machine intelligence, are outlined as well.*
-------------------------------------------------------------------------------------------**06.03.2024 | 15:40 | Tommaso Lando**

*University of Bergamo, Italy*

**Title: Testing second-order stochastic dominance***Given samples from two non-negative random variables, we propose a new class of nonparametric tests for the null hypothesis that one random variable dominates the other with respect to second-order stochastic dominance. These tests are based on the Lorenz P-P plot (LPP), which is the composition between the inverse unscaled Lorenz curve of one distribution and the unscaled Lorenz curve of the other. The LPP exceeds the identity function if and only if the dominance condition is violated, providing a rather simple method to construct test statistics, given by functionals defined over the difference between the identity and the LPP. We determine a stochastic upper bound for such test statistics under the null hypothesis, and derive its limit distribution, to be approximated via bootstrap procedures. We also establish the asymptotic validity of the tests under relatively mild conditions, allowing for both dependent and independent samples. Finally, finite sample properties are investigated through simulation studies.*
-------------------------------------------------------------------------------------------~~20.03.2024~~21.03.2024 | 15:40 | Anthony Davison

*Swiss Federal Institute of Technology in Lausanne*

**Title: A statistical approach to conjunction assessment***Satellite conjunctions involving “near misses” of space objects are becoming increasingly likely. One approach to risk analysis for them involves the computation of the collision probability, but this has been regarded as having some counterintuitive properties and its interpretation has been debated. This talk formulates an approach to satellite conjunction based on a simple statistical model and discusses inference on the miss distance between the two objects, both when the relative velocity can be taken as known and when its uncertainty must be taken into account. The usual collision probability estimate can be badly biased, but highly accurate inference on the miss distance is possible. The ideas are illustrated with case studies and Monte Carlo results that show its excellent performance. The work is joint with Soumaya Elkantassi.*
-------------------------------------------------------------------------------------------**03.04.2024 | 15:40 | Zuzana Rošťáková**

*Slovak Academy of Sciences, Slovakia*

**Title: Tensor decomposition as a useful tool for EEG analysis***Tensor decomposition is a powerful tool when detecting latent structure in higher-order arrays, especially in chemometrics or psychology. In neurophysiology, tensor decomposition has only been receiving attention in the last couple of decades. Our presentation provides an overview of tensor decomposition methods that can successfully reveal the latent structure of the human electroencephalogram (EEG) recorded during the neurorehabilitation of post-stroke patients. Despite their flexibility and natural interpretation of EEG decomposition, tensor decomposition has several drawbacks, especially selecting the appropriate number of latent components. The advantages and disadvantages of tensor decomposition will be demonstrated on real-world and simulated EEG data with known properties. Finally, we will focus on the potential application of tensor decomposition for the detection and removal of EEG artifacts.*
-------------------------------------------------------------------------------------------**17.04.2024 | 15:40 | Annika Betken**

*University of Twente, Netherlands*

**Title: Ordinal/Depth patterns in time series analysis***or univariate time series, ordinal patterns describe the relative positions of consecutive observations generated by an underlying data-generating stochastic process. Since, accordingly, a definition of ordinal patterns presupposes a total ordering of observations, there is, however, no straightforward extension of this notion to multivariate data. A lack of canonical ordering of $\mathbb{R}^d$ can be overcome by the concept of statistical depth, i.e. by measuring how deep a data point lies in a given reference distribution. The corresponding center-outward ordering of observations in multivariate time series data naturally leads to the definition of ordinal patterns for multivariate data (depth patterns). We consider estimators for the probabilities of occurrence of ordinal patterns in univariate time series and and depth patterns in multivariate time series. In the univariate case, we investigate statistical properties of these estimators for discrete-time Gaussian processes with stationary increments. Limit theorems that describe the asymptotic distribution of the considered estimators are established. Depending on the behavior of the data generating processes' autocorrelation function, these limit distributions differ. In the multivariate case, depending on the choice of reference distribution and the relation between reference and data distribution, we distinguish different settings that are considered separately. Within these settings we study statistical properties of depth pattern probabilities, establishing consistency and asymptotic normality in specific cases under the assumption of weakly dependent time series data.*
-------------------------------------------------------------------------------------------**15.05.2025 | 15:40 | Eugen Pircalabelu**

*Université catholique de Louvain, Belgium*

**Title: Unbalanced distributed estimation and inference for (covariate-adjusted) Gaussian graphical models***A distributed estimation and statistical inference framework is introduced for the sparse precision matrix in the (covariate-adjusted) Gaussian graphical models under the unbalanced splitting setting. This type of splitting arises when the datasets from different sources cannot be aggregated on one single machine or when the available machines are of different powers. A de-biased estimator of the precision matrix on every single machine is proposed, and theoretical guarantees are provided. Moreover, a new de-biased estimator that is pooled across the machines using a composite likelihood approach is proposed. It is shown to enjoy consistency and asymptotic normality, and we provide statistical inference strategies based on it. The performance of this estimator is investigated via simulation studies and real data examples. It is shown that the performance of this estimator is close to the non-distributed estimator, which uses the entire dataset.*
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