Recently it was shown through simulations studies that Sub-D produces estimates with unbiased and lower variance-covariance estimates than the ANOVA-based estimator, except in case of random “one-way” balanced designs. In this designs the simulations studies suggested they have the same variance-covariance estimates. This paper aims to compare the common ANOVA-based estimator to Sub-D in random “one-way” designs with two groups of treatment and in random “one-way” balanced designs. The comparison will be conducted through theoretical results and corroborated with simulation studies. It will be proved that the ANOVA-base estimator and Sub-D have exactly the same variance-covariance estimates in both above referred designs. The proof will be given firstly for random “one-way” designs with two groups of treatment and then for random “one-way” balanced designs.

In recent years, matrix-valued data has received an increasing amount of attention. This is due to their frequent application in various fields, such as signal processing, finance, medicine, engineering, among others. Here we consider matrix-valued time series processes and our aim is to detect changes in the mean behavior.

An obvious way to handle the problem is to make use of vectorization, i.e. the columns of the matrix are written together as a matrix. The problem is then reduced to the detection of a change in a vector time series. Such problems have been discussed by, e.g. Kramer and Schmid (1997), Bodnar et al. (2023), and Bodnar et al. (2024). The disadvantage of vectorization consists in the fact that the resulting time series process may be high-dimensional and the process identification is quite difficult.

In the last five years, other types of matrix-valued time series processes have been proposed (e.g., Chen et al. (2021), Wu and Bi (2023)). These approaches are characterized by fewer parameters and, for that reason, are of great interest in practice.

Using these new types of time series model, EWMA control charts for matrix-valued time series are derived. The control design is calculated, and some explicit results are given for matrix-valued autoregressive processes. The performance of the charts is compared with each other within an extensive simulation study.

Joint work with:

• S. Knoth, Department of Economics and Social Sciences, Institute of Mathematics and Statistics, Helmut Schmidt University, Hamburg, Germany
• Y. Okhrin, Department of Statistics and Data Science, Faculty of Business and Economics, University of Augsburg, Germany
• V. Petruk, Department of Statistics, Faculty of Business Administration and Economics, European University Viadrina, Frankfurt (Oder), Germany

When an accurate representation of multivariate data is required across both the body (described by non-extreme observations) and the tail (defined by the extreme observations) regions, it is crucial to have a model that is able to characterise the joint behaviour across both regions. In this work, we propose dependence models that represent the entire distribution without the need to explicitly define each region. We do so by constructing copulas that are based on mixture distributions defi ned on the full support of the data. For such models, we derive (sub)-asymptotic dependence properties for specific model configurations, and show that they are flexible in capturing a broad range of extremal dependence structures through simulation studies. Motivated by the computational resources required to evaluate the likelihood function of the proposed models, we also explore likelihood-free approaches that use neural networks to perform inference. In particular, we assess the performance of neural Bayes estimators in estimating the model parameters, both for one of the models introduced for the joint body and tail, and further complex extremal dependence models. We also propose a neural Bayes classifier for model selection. In this way, we provide a toolbox for simple fitting and model selection of complex extremal dependence models.

Joint work with: Jennifer Wadsworth, Jonathan Tawn, Raphaël Huser and Adrian O’Hagan.

Since the coined question in 1986 “Can a set of weak learners create a single strong learner?”, ensemble learning has been focused on merging simple machine learning methods in order to increase predictive performance. Characteristics such as stability and diversity are important to choose these weak learners in bagging procedure. In the same field, Support Vector Models (SVM) are strong and stable learners which have been drawing the attention of the community once these models have some properties which are easy to characterize and at the same time provide an estimation process with global optimization properties. In this talk, we present the Random Machines method. A new machine learning method based on SVM ensemble learning which exposes how a set of strong learners can create a single stronger learner.

Recent years have seen remarkable progress in Monte Carlo simulation methods, driven by the integration of cutting-edge machine learning techniques such as Generative Adversarial Networks (GANs), diffusion models, and normalizing flows. These innovations enable the generation of complex, high-dimensional data, from highly realistic human faces to artistic transformations, such as converting a landscape photo into a Van Gogh-style painting. These breakthroughs, which often make headlines, capture widespread interest but remain challenging to simulate using traditional Monte Carlo techniques. GANs operate by training two networks in a competitive framework, yielding impressive results in high-dimensional sampling. Diffusion models offer a compelling alternative to Monte Carlo sampling by iteratively refining samples, reversing a noise-adding process, and producing smooth transitions critical for many applications. Normalizing flows map simple, tractable distributions (e.g., Gaussians) to complex target distributions through a sequence of invertible transformations, enabling efficient density estimation and sample generation. These advancements significantly expand the scope of Monte Carlo simulations, allowing statisticians and researchers to model more complex and non-standard distributions with greater accuracy and computational efficiency. This talk will explore these transformative methods, highlighting their principles, applications, and potential to redefine simulation in modern statistics and data science.