This seminars series is dealing with the topic of the mathematics applied to extremes, risk, climate and environment. As one aim of this seminar series is to openly cross-pollinate research on extreme values, the organizers also welcome suggestions of speakers from anyone. So, feel free to drop names suggestions to the organizers.
The seminar will take place at the Jussieu campus of Sorbonne University or at the LSCE of Universite Paris Saclay and on Zoom with permanent link, pwd ERCE2022.
- January 18 14h-15h: Hansjoerg Albrecher (Lausanne University)
Postponed (likely in April-May when Covid could be well under control again...)
- January 18 11h30 - 12h30: Maud Thomas (LPSM, Paris)
Salle du Séminaire du LMV (Bâtiment Fermat), UFR des Sciences, Versailles
Temporary Zoom link ID: 958 3609 1855 pw: 268194
Title : Non-asymptotic bounds for probability weighted moments estimators
Abstract : In hydrology and other applied fields, Probability Weighted Moments (PWM) have been frequently used to estimate the parameters of classical extreme value distributions. This method-of-moments technique can be applied when second moments are finite, a reasonable assumption in hydrology. Two advantages of PWM estimators are their ease of implementation and their close connection to the well-studied class of U-statistics. Consequently, precise asymptotic properties can be deduced. In practice, sample sizes are always finite and, depending on the application at hand, the sample length can be small, e.g. a sample of only 30 years of daily precipitation is quite common in some regions of the globe. In such a context, asymptotic theory is on a shaky ground and it is desirable to get non-asymptotic bounds. Deriving such bounds from off-the-shelf techniques (Chernoff method) requires exponential moment assumptions, which are unrealistic in many settings. To bypass this hurdle, we propose a new estimator for PWM, inspired by the median-of-means framework of Devroye-Lerasle-Lugosi-Oliveira (AoS 2016). This estimator is then shown to satisfy a sub-Gaussian inequality, with only second moment assumptions. This allows us to derive non-asymptotic bounds for the estimation of the parameters of extreme value distributions and of extreme quantiles. (joint work with A. Ben-Hamou and P. Naveau)
- February 4 14h-15h: Gloria Buriticá (Sorbonne University)
salle 1129 (Bat 714), LSCE, Université Paris-Saclay and Zoom (see the permanent link above)
Title: Stable sums to infer high return levels of multivariate rainfall time series
Abstract: We introduce the stable sums method for inference of extreme return levels for multivariate stationary time series. This new method is based on large deviation principles for regularly varying time series which allows for incorporation of time and space extreme dependencies in the analysis. It avoids classical declustering steps as implementation coincides for both independent and dependent observations from the stationary model. A comparison with the main estimators from extreme value theory, where detecting clustering in time is required, shows improvement of the coverage probabilities of confidence intervals obtained from our method against its competitors. Numerical experiments also point to a smaller mean squared error with the multivariate stable sums method compared to an univariate approach. We apply our method for inference of high return levels of multivariate daily fall precipitation measurements in France.
- Anne Sabourin (TélécomParis) February 16 14h – 15h TBA
- 2 week graduate classes (7-18 March, in Paris IHP)
with lectures by Prof. Anja Janßen, Prof. Daniela Casto Camilo and Prof. Valérie Chavez
- November 24, 14h-15h: Marco Oesting (Stuttgart University)
Title: Estimation of the spectral measure from convex combinations of regularly varying random vectors.
- December 1, 14h-15h: Ioannis Papastathopoulos (Edinburgh University)
Title: Statistical modelling of time series extremes.
Slides and recording
The organizing committee, i.e.
- Philippe Naveau (LSCE, Gif)
- Maud Thomas (LPSM, Sorbonne Université)
- Olivier Wintenberger (LPSM, Sorbonne Université)