Gloria Buriticá

Gloria Buriticá

I'm a lecturer in statistics at MIA Paris-Saclay, AgroParisTech. My research is centered on extreme value theory and statistical learning with a primary focus on risk assessment in climate sciences.

Publications

Progression: an extrapolation principle for regression

Published in Submitted, 2024

Leveraging the theory of tail dependence, this article presents a method for regression extrapolation to predict beyond the observed data range. To achieve this, we derive suitable restrictions on the regression function at the boundary of the training sample. These conditions holds for a wide range of models including non-parametric regression functions with additive noise. Moreover, we establish approximation error guarantees quantifying how far we can extrapolate with a function veryfing these boundary constrains. This results justify our learning strategy, which focuses on learning the constraints and applying them to produce reliable extrapolation predictions.

Recommended citation: G. Buritica, Progression: an extrapolation principle for regression. arXiv:2410.23246. https://doi.org/10.1007/s10687-024-00499-9

Modeling Extreme Events: Univariate and Multivariate Data-Driven Approaches

Published in Submitted, 2024

This note presents data-driven methodologies for risk analysis based on univariate and multivariate methods in extreme value theory. It contains the contribution of team genEVA for the 2023 EVA data challenge competition organized in Milano.

Recommended citation: G. Buritica, M. Hentschel, O. C. Pasche, F. Roettger, Z. Zhang (2024). Modeling extreme events: Univariate and multivariate data-driven approaches. Extremes. https://doi.org/10.1007/s10687-024-00499-9

Large deviations of lp-blocks of regularly varying time series and applications to cluster inference

Published in Stochastic processes and their applications, 2023

This paper studies large deviations of p-norms of stationary regularly varying time series. It introduces α-clusters, where α is the tail-index of the series, and proposes consistent disjoint blocks estimators of α-cluster features. This new methodology proves to be robust to handle time dependencies.

Recommended citation: G. Buriticá, T. Mikosch, O. Wintenberger. (2023). Large deviations of lp-blocks of regularly varying time series and applications to cluster inference. *Stochastic Processes and their Applications*. **161**, 68--101. https://doi.org/10.1016/j.spa.2023.03.013

On the asymptotics of extremal lp-blocks cluster inference

Published in Submitted, 2022

Recently, we proposed a new estimator for cluster inference for heavy-tailed time series. This paper states the asymptotic normality of our α-cluster-based estimator. We infer the extremal index, the cluster lengths and other important indices in extremes. Also, we compute the asymptotic variances for ARMA models and stochastic recurrence equations, which shows our estimator compares favourably with classical approaches in terms of variance.

Recommended citation: G. Buriticá, O. Wintenberger. (2022). On the asymptotics of extremal lp-blocks cluster inference. https://arxiv.org/abs/2212.13521

Stable sums to infer high return levels of multivariate rainfall time series

Published in Environmetrics, 2022

This paper presents the stable sums method to infer high return levels of multivariate heavy-tailed time series. This new method is justified by the large deviations of powers of α-sums, where α is the tail-index of the series. Its main advantage is that is implementation coincides for dependent and independent time series.

Recommended citation: G. Buriticá, P. Naveau. (2022). Stable sums to infer high return levels of multivariate rainfall time series, Environmetrics, e2782. https://doi.org/10.1002/env.2782

Some variations of the extremal index

Published in Zap. Nauchn. Semin. POMI. Volume 501, Probability and Statistics, 2021

This paper is an overview on the extremal index for stationary time series. It provides a new interpretation in terms of α-clusters, where α is the tail-index of the series.

Recommended citation: G. Buriticá, N. Meyer, T. Mikosch, O. Wintenberger. (2021). Some variations of the extremal index. Zap. Nauchn. Semin. POMI. Volume 501, Probability and Statistics.* **30**, 52—77. To be translated in J.Math.Sci. (Springer). https://arxiv.org/abs/2106.05117