Extremal behaviour of aggregated data with an application to downscaling

Engelke, Sebastian; Fondeville, Raphaël de; Oesting, Marco

doi:10.1093/biomet/asy052

Cited by 27 publications

(32 citation statements)

References 39 publications

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“…data, in our setting we want to penalize the variation of the shape function 𝑥 ↦ → 𝜉 (𝑥) across the predictor space X. In spatial applications, for instance, it is common to assume a constant shape parameter at different locations (e.g., Ferreira et al, 2012;Engelke et al, 2019). Similarly, in ERF we shrink the estimates ξ (𝑥) to a constant shape parameter 𝜉 0 .…”

Section: Penalized Log-likelihoodmentioning

confidence: 99%

Extremal Random Forests

Gnecco¹,

Terefe²,

Engelke³

2022

Preprint

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Classical methods for quantile regression fail in cases where the quantile of interest is extreme and only few or no training data points exceed it. Asymptotic results from extreme value theory can be used to extrapolate beyond the range of the data, and several approaches exist that use linear regression, kernel methods or generalized additive models. Most of these methods break down if the predictor space has more than a few dimensions or if the regression function of extreme quantiles is complex. We propose a method for extreme quantile regression that combines the flexibility of random forests with the theory of extrapolation. Our extremal random forest (ERF) estimates the parameters of a generalized Pareto distribution, conditional on the predictor vector, by maximizing a local likelihood with weights extracted from a quantile random forest. Under certain assumptions, we show consistency of the estimated parameters. Furthermore, we penalize the shape parameter in this likelihood to regularize its variability in the predictor space. Simulation studies show that our ERF outperforms both classical quantile regression methods and existing regression approaches from extreme value theory. We apply our methodology to extreme quantile prediction for U.S. wage data.

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Section: Penalized Log-likelihoodmentioning

confidence: 99%

Extremal Random Forests

Gnecco¹,

Terefe²,

Engelke³

2022

Preprint

Self Cite

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“…where θ r ≥ 0 is the r-extremal coefficient (Engelke et al, 2019a). Its theoretical value is known beforehand in some cases, such as for the mean aggregation where θ r = 1, but in other cases it depends on the (unknown) extremal dependence structure.…”

Section: Limitations Of Naive Resamplingmentioning

confidence: 99%

Semi-parametric resampling with extremes

2021

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Nonparametric resampling methods such as Direct Sampling are powerful tools to simulate new datasets preserving important data features such as spatial patterns from observed or analogue datasets while using only minimal assumptions. However, such methods cannot generate extreme events beyond the observed range of data values. We here propose using tools from extreme value theory for stochastic processes to extrapolate observed data towards yet unobserved high quantiles. Original data are first enriched with new values in the tail region, and then classical resampling algorithms are applied to enriched data. In a first approach to enrichment that we label "naive resampling", we generate an independent sample of the marginal distribution while keeping the rank order of the observed data. We point out inaccuracies of this approach around the most extreme values, and therefore develop a second approach that works for datasets with many replicates. It is based on the asymptotic representation of extreme events through two stochastically independent components: a magnitude variable, and a profile field describing spatial variation. To generate enriched data, we fix a target range of return levels of the magnitude variable, and we resample magnitudes constrained to this range. We then use the second approach to generate heatwave scenarios of yet unobserved magnitude over France, based on daily temperature reanalysis training data for the years 2010 to 2016.

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“…In terms of statistical inference and modeling, the recent work of de Fondeville and his colleagues (see, e.g., de Fondeville and Davison, 2019Davison, , 2018Engelke et al, 2019) could also help to build multivariate Pareto processes in time, space or both.…”

Section: Multivariate Evtmentioning

confidence: 99%

Statistical Methods for Extreme Event Attribution in Climate Science

Naveau

Hannart

Ribes

2020

Annu. Rev. Stat. Appl.

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Changes in the Earth's climate have been increasingly observed. Assessing the likelihood that each of these changes has been caused by human influence is important for decision making on mitigation and adaptation policy. Because of their large societal and economic impacts, extreme events have garnered much media attention—have they become more frequent and more intense, and if so, why? To answer such questions, extreme event attribution (EEA) tries to estimate extreme event likelihoods under different scenarios. Over the past decade, statistical methods and experimental designs based on numerical models have been developed, tested, and applied. In this article, we review the basic probability schemes, inference techniques, and statistical hypotheses used in EEA. To implement EEA analysis, the climate community relies on the use of large ensembles of climate model runs. We discuss, from a statistical perspective, how extreme value theory could help to deal with the different modeling uncertainties. In terms of interpretation, we stress that causal counterfactual theory offers an elegant framework that clarifies the design of event attributions. Finally, we pinpoint some remaining statistical challenges, including the choice of the appropriate spatio-temporal scales to enhance attribution power, the modeling of concomitant extreme events in a multivariate context, and the coupling of multi-ensemble and observational uncertainties.

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Extremal behaviour of aggregated data with an application to downscaling

Cited by 27 publications

References 39 publications

Extremal Random Forests

Extremal Random Forests

Semi-parametric resampling with extremes

Statistical Methods for Extreme Event Attribution in Climate Science

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