(NMST611) Advanced Statistical Seminar 2024/2025
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)
- 02.10.2024 | 15:40 | Krzysztof Podgórski
Lund University, Sweden
Title: Orthogonal Splines and Inversion of Sparse Matrices
A dyadic algorithm for diagonalizing an arbitrary positive definite band matrix (a band Gramian) is obtained to efficiently orthogonalize the B-splines. In the algorithm, the sparsity of a band Gramian is utilized to produce a natural dyadic net of orthogonal splines, rather than a sequence of them. Such a net is thus naturally referred to as a splinet. The splinets exploit “near-orthogonalization” of the B-splines and feature locality expressed and computational efficiency that is a result of a small number of required inner product evaluations. Inverting sparse matrices of large dimensions is a problem that one often faces in high-dimensional statistical analysis, spatial econometrics, algebraic and differential equations, or numerical analysis. The main challenge is how to utilize the sparsity to make an efficient inversion. Dealing with the challenge in full generality seems to be not feasible due to the numerical complexity. However, if one assumes that the sparsity features some structural form, one can search for a suitable inversion method that utilizes this structure. Here, an efficient algorithm is obtained for the inversion of sparse matrices that have a dyadic structure. The dyadic algorithm for the orthogonalization of the $B$-splines has been extended for this purpose and its computational complexity is assessed. A separate algorithm leading to packing a sparse matrix into a dyadic form is also obtained.
------------------------------------------------------------------------------------------- - 16.10.2024 | 15:40 | Yarema Okhrin
Universität Augsburg, Germany
Title: Consistent Estimation of the High-Dimensional Efficient Frontier
In this paper, we analyze the asymptotic behavior of the main characteristics of the mean-variance efficient frontier employing random matrix theory. Our particular interest covers the case when the dimension $p$ and the sample size $n$ tend to infinity simultaneously and their ratio $p/n$ tends to a positive constant $c\in(0,1)$. We neither impose any distributional nor structural assumptions on the asset returns. For the developed theoretical framework, some regularity conditions, like the existence of the $4$th moments, are needed. It is shown that two out of three quantities of interest are biased and overestimated by their sample counterparts under the high-dimensional asymptotic regime. This becomes evident based on the asymptotic deterministic equivalents of the sample plug-in estimators. Using them we construct consistent estimators of the three characteristics of the efficient frontier. It it shown that the additive and/or the multiplicative biases of the sample estimates are solely functions of the concentration ratio $c$. Furthermore, the asymptotic normality of the considered estimators of the parameters of the efficient frontier is proved. Verifying the theoretical results based on an extensive simulation study we show that the proposed estimator for the efficient frontier is a valuable alternative to the sample estimator for high dimensional data. Finally, we present an empirical application, where we estimate the efficient frontier based on the stocks included in S\&P 500 index.
------------------------------------------------------------------------------------------- - 30.10.2024 | 15:40 | Tomáš Hobza
Czech Technical University in Prague, Czech Republic
Title: Small area estimation – introduction, models and real data application
Small Area Estimation (SAE) is a branch of mathematical statistics that deals with the problem of estimating population parameters in subsets (called areas or domains) of a population where the sample sizes are not large enough to provide reliable direct estimates. For this purpose, SAE introduces statistical models that “borrow strength” from related small areas, data from external administrative sources, or data from different time periods. An overview of basic principles, models and problems encountered in SAE is given in the first part of the presentation. Then, the ideas are illustrated by an application of a unit-level multinomial mixed model to real data from the first Spanish Labour Force Survey of 2021, where the target is to map labour force indicators by province, sex, and age group.
------------------------------------------------------------------------------------------- - 13.11.2024 | 15:40 | Gauthier Thurin
Institut de Mathématiques de Bordeaux, France
Title: Multivariate quantiles and superquantiles
We introduce center-outward superquantile and expected shortfall functions, to characterize multivariate tail probabilities and central areas of point clouds. These notions build up on a multivariate quantile function based on measure transportation ideas. They characterize the underlying distributions and their weak convergence, which underlines their importance. Finally, these definitions will be applied to risk analysis, with multivariate definitions of Value-at-Risk and Conditional-Value-at-Risk.
------------------------------------------------------------------------------------------- - 27.11.2024 | 15:40 | Geurt Jongbloed
Delft University of Technology, The Netherlands
Title: Wicksell’s problem -- New results in the classical and extended model
Wicksell’s problem was posed almost a century ago in 1925 as “the corpuscle problem” by Sven Wicksell in Biometrika. It is a model where spheres of (iid) random sizes are distributed within a 3D opaque medium according to a homogeneous Poisson Process. Cutting the medium in two by a plane, reveals circular profiles of random sizes. The main problem is then to obtain the distribution of the sphere sizes, being only able to see the circle radii. The problem is an example of a stereological problem. Statistically, it is an inverse problem. Wicksell already derived the distribution of the observable circle radii in terms of that of the underlying sphere radii. There is also an explicit inverse transformation, expressing the distribution of interest in terms of that of the observables. In this presentation, we will present recently found adaptivity properties of the so-called isotonic inverse estimator in the classical problem, where the 3D particles are spheres. We will also introduce a more general formulation of the model, where the particles are more general convex bodies (all of the same shape, with random sizes). That model is also an inverse problem, but the transformations cannot be analytically written down in integral transforms. Some need to be approximated via simulation. We will present some properties of the model and introduce a consistent likelihood based estimator.
------------------------------------------------------------------------------------------- - 11.12.2024 | 15:40 | Valentina Masarotto
Universiteit Leiden, The Netherlands
Title: Second order inference for functional data: where covariance operators meet Mandarin Chinese
All forms of verbal interaction and communication include melodic components. Volume and intonation express emotions, imply jokes, questions, and overall shape the meaning of a message. Such melodic variations assume an even more dramatic role in tonal languages, as, in this setting, varying a sound's pitch while pronouncing the same word conveys different lexical meanings. An interesting aspect of tonal languages is tonal coarticulation, appearing when tones are concatenated to one another and affect each other. How can we study it? A large part of phonetic analysis is based on speech recording, and focusses on modelling fundamental frequency curves, whose intrinsic smooth structure identifies them naturally as functional data. Within the FDA domain, covariance operators are key players, and can themselves be the subject of statistical inference. Statistics on covariances however, is impaired by both their infinite-dimensionality and their intrinsic non-linearity. Despite the challenges, working within such non-linearity constraints, can give rise to very powerful procedures. Inspired by the problem of modelling the effect of tonal coarticulation, this talk will link to optimal transport and discuss the mathematics behind powerful inferential tool for covariances.
------------------------------------------------------------------------------------------- - 08.01.2025 | 15:40 | Anne Sabourin
Université Paris Cité, France
Title: Statistical learning with extreme covariates
Extreme Value Analysis is a branch of probability and statistics focused on the tail behavior of random processes, namely on limiting distributions of rescaled excesses above high thresholds. In applications (typically, finance or environmental sciences), such tail processes encapsulate crucial features for risk management, e.g. the dependence relationships between tail events such as an excess over a high threshold in different components. This talk will provide an overview of a recent line of work aiming at establishing non-asymptotic guarantees on estimators and machine learning algorithms dedicated to learning key features of tail behaviors. We shall focus in particular on the problem of `learning on extreme covariates' and review recent advances and open research directions.
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Advanced Statistical Seminar (Archiv)
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The archive of the guests (invited speakers) of the Advanced statistical seminar (NMST611)
from previous semesters together with the title of the talks and short abstracts. |
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| Winter term 2023/2024 | Summer term 2024 |
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| Summer term 2023 | |
| Summer term 2022 | |
| Summer term 2021 | |
