Pokročilý statistický seminář
Wednesday, 3:40 PM CET (odd weeks of semester)
Streda 15:40 Praktikum KPMS (liché týdny semestru)
(Universität Heidelberg, via Zoom)
Abstract: In this talk, we study the problems of additive and multiplicative deconvolution in the context of statistical inverse problems. We will begin with an introduction to statistical inverse problems and consider then the two deconvolution problems. Using a spectral cut-off regularisation of the inverse of the Fourier transform, respectively the Mellin transform, we deduce estimators for both models and analyse their statistical properties. More precisely, we will show that both estimators are minimax-optimal for a suitable choice of the cut-off parameter. We finish the talk by illustrating the behaviour of the proposed estimators using a Monte-Carlo simulation.
(Imperical College London)
Abstract: Kernel-based statistical methods have become a mainstay of statistical machine learning in the past two decades and have also seen application in other statistical areas, such as computational statistics. The idea is to use kernels to formulate discrepancies between probability measures in a way which is easy to estimate. Specific applications include two-sample testing, independence testing, goodness-of-fit testing, parameter inference, measure transport and MCMC output quality assessment. So far, most investigation of these methods has focused on Euclidean data. In this talk I will outline our work generalising these methods to the generality of samples lying in a separable Hilbert space. This opens the door to apply these methods to functional data. Along the way I will draw connections between innovations in functional data analysis and kernel-based methods and provide numerical examples of kernel-based methods on functional data.
(University of Alberta and Charles University)
Predikcia poistných rezerv: metódy založené na funkcionálnych profiloch
Abstract: One of the most fundamental tasks in non-life insurance, done on regular basis, is risk reserving assessment analysis, which amounts to predict stochastically the overall loss reserves to cover possible claims. The most common reserving methods are based on different parametric approaches using aggregated data structured in the run-off triangles. In this paper, we propose rather a non-parametric approach, where the underlying loss development triangles and the subsequent reserves predictions are handled as functional data. A suitable bootstrap add-on is developed to obtain the whole reserves distribution in accordance with the standard regulatory guidelines used in the industry. Three competitive functional- based reserving techniques, each with slightly different scope, are introduced; their theoret- ical and practical advantages—in particular, effortless implementation, robustness against outliers, and wide-range applicability—are discussed. The real run-off triangles are used to evaluate the empirical performance of the designed methods and a full scale comparison with standard (parametric) reserving techniques is carried on. The overall claims reserving performance is evaluated with respect to the known real loss outcomes. The important objective of the paper is also to promote the idea of natural usefulness of the functional reserving methods among the reserving practitioners.
(McGill University, Montréal)
Abstract: In this talk, I will present a model that can account for any type of asymptotic dependence between extremes while capturing joint risks at medium levels. It is characterized by a multivariate stable tail dependence function and a univariate parametric distortion function, which is the Archimedean generator of the underlying Archimax copula. The model can be fitted using a semi-parametric procedure in which the distortion function is first fitted using a rank-based moment technique, and the stable tail dependence function is subsequently estimated nonparametrically. The estimators are asymptotically Gaussian under broad regularity conditions. The model will be employed to analyze monthly rainfall maxima in French Brittany. Its application reveals an asymmetry of the underlying stable tail dependence function, which can be explained by causal relationships between precipitation in different areas. As we will see, the model can also be extended in a hierarchical fashion to capture more complex dependence patters between a larger number of stations.
This talk is based on joint work with Simon Chatelain and Anne-Laure Fougères.
(Imperical College London)
Abstract: Kernel-based statistical methods have become a mainstay of statistical machine learning in the past two decades and have also seen application in other statistical areas, such as computational statistics. The idea is to use kernels to formulate discrepancies between probability measures in a way which is easy to estimate. Specific applications include two-sample testing, independence testing, goodness-of-fit testing, parameter inference, measure transport and MCMC output quality assessment. So far, most investigation of these methods has focused on Euclidean data. In this talk I will outline our work generalising these methods to the generality of samples lying in a separable Hilbert space. This opens the door to apply these methods to functional data. Along the way I will draw connections between innovations in functional data analysis and kernel-based methods and provide numerical examples of kernel-based methods on functional data.
Pondelok 15:40 K11
Podmienky pre získanie zápočtu
Všetky výukové materiály budú prístupné na Moodle UK;
detaily nájdete na hlavnej stránke cvičení.
Zápočtová písomka: Výsledky v SISe
R skripty:
Dáta:
Tuesday 17:20 K4
For general information about the exercise sessions and the credit requirements see the main website of the exercise sessions.
The final test takes place on Thursday, December 16, from 17:20 in K4.
Details can be found here.
Homework assignments:
R scripts used at the lab sessions
Datasets:
Some useful documents: