arXiv subjects

Gloria Buriticá

Publications and source records attributed to Gloria Buriticá.

6 recordsLinked to original sources

arXiv2025

On the asymptotics of extremal lp-blocks cluster inference

Extremes occur in stationary regularly varying time series as short periods with several large observations, known as extremal blocks. We study cluster statistics summarizing the behavior of functions acting on these extremal blocks. Examples of cluster statistics are the extremal index, cluster size probabilities, and other cluster indices. The purpose of our work is twofold. First, we state the asymptotic normality of block estimators for cluster inference based on consecutive observations with large lp-norms, for p < 0. The case p=$α$, where $α$ > 0 is the tail index of the time series, has specific nice properties thus we analyze the asymptotic of blocks estimators when approximating $α$ using the Hill estimator. Second, we verify the conditions we require on classical models such as linear models and solutions of stochastic recurrence equations. Regarding linear models, we prove that the asymptotic variance of classical index cluster-based estimators is null as first conjectured in Hsing T. [26]. We illustrate our findings on simulations.

math.PR↗

arXiv2024

Progression: an extrapolation principle for regression

The problem of regression extrapolation, or out-of-distribution generalization, arises when predictions are required at test points outside the range of the training data. In such cases, the non-parametric guarantees for regression methods from both statistics and machine learning typically fail. Based on the theory of tail dependence, we propose a novel statistical extrapolation principle. After a suitable, data-adaptive marginal transformation, it assumes a simple relationship between predictors and the response at the boundary of the training predictor samples. This assumption holds for a wide range of models, including non-parametric regression functions with additive noise. Our semi-parametric method, progression, leverages this extrapolation principle and offers guarantees on the approximation error beyond the training data range. We demonstrate how this principle can be effectively integrated with existing approaches, such as random forests and additive models, to improve extrapolation performance on out-of-distribution samples.

stat.ME↗

arXiv2024

Modeling Extreme Events: Univariate and Multivariate Data-Driven Approaches

This article summarizes the contribution of team genEVA to the EVA (2023) Conference Data Challenge. The challenge comprises four individual tasks, with two focused on univariate extremes and two related to multivariate extremes. In the first univariate assignment, we estimate a conditional extremal quantile using a quantile regression approach with neural networks. For the second, we develop a fine-tuning procedure for improved extremal quantile estimation with a given conservative loss function. In the first multivariate sub-challenge, we approximate the data-generating process with a copula model. In the remaining task, we use clustering to separate a high-dimensional problem into approximately independent components. Overall, competitive results were achieved for all challenges, and our approaches for the univariate tasks yielded the most accurate quantile estimates in the competition.

stat.ME↗

arXiv2022

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

In the regularly varying time series setting, a cluster of exceedances is a short period for which the supremum norm exceeds a high threshold. We propose to study a generalization of this notion considering short periods, or blocks, with lp-norm above a high threshold. Our main result derives new large deviation principles of extremal lp-blocks, which guide us to define and characterize spectral cluster processes in lp. We then study cluster inference in lp to motivate our results. We design consistent disjoint block estimators to infer features of cluster processes. Our estimators promote the use of large empirical quantiles from the lp-norm of blocks as threshold levels which eases implementation and also facilitates comparison for different p>0. Our approach highlights the advantages of cluster inference based on extremal l$α$--blocks, where $α$>0 is the index of regular variation of the series. We focus on inferring important indices in extreme value theory, e.g., the extremal index.

math.PR↗

arXiv2022

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

Heavy rainfall distributional modeling is essential in any impact studies linked to the water cycle, e.g.\ flood risks. Still, statistical analyses that both take into account the temporal and multivariate nature of extreme rainfall are rare, and often, a complex de-clustering step is needed to make extreme rainfall temporally independent. A natural question is how to bypass this de-clustering in a multivariate context. To address this issue, we introduce the stable sums method. Our goal is to incorporate time and space extreme dependencies in the analysis of heavy tails. To reach our goal, we build on large deviations of regularly varying stationary time series. Numerical experiments demonstrate that our novel approach enhances return levels inference in two ways. First, it is robust concerning time dependencies. We implement it alike on independent and dependent observations. In the univariate setting, it improves the accuracy of confidence intervals compared to the main estimators requiring temporal de-clustering. Second, it thoughtfully integrates the spatial dependencies. In simulation, the multivariate stable sums method has a smaller mean squared error than its component-wise implementation. We apply our method to infer high return levels of daily fall precipitation amounts from a national network of weather stations in France.

stat.ME↗

arXiv2021

Some variations on the extremal index

We re-consider Leadbetter's extremal index for stationary sequences. It has interpretation as reciprocal of the expected size of an extremal cluster above high thresholds. We focus on heavy-tailed time series, in particular on regularly varying stationary sequences, and discuss recent research in extreme value theory for these models. A regularly varying time series has multivariate regularly varying finite-dimensional distributions. Thanks to results by Basrak and Segers we have explicit representations of the limiting cluster structure of extremes, leading to explicit expressions of the limiting point process of exceedances and the extremal index as a summary measure of extremal clustering. The extremal index appears in various situations which do not seem to be directly related, like the convergence of maxima and point processes. We consider different representations of the extremal index which arise from the considered context. We discuss the theory and apply it to a regularly varying AR(1) process and the solution to an affine stochastic recurrence equation

math.PR↗