Local Likelihood Estimation of Complex Tail Dependence Structures, Applied to U.S. Precipitation Extremes

Castro‐Camilo, Daniela; Huser, Raphaël

doi:10.1080/01621459.2019.1647842

Cited by 29 publications

(17 citation statements)

References 59 publications

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“…Therefore, we always need to choose a finite, and often relatively small, block size, which casts doubts on the validity of the max‐stability assumption in practice. A fast growing body of empirical studies on environmental extremes in the literature has indeed revealed that the max‐stability assumption arising asymptotically is often violated at finite levels (Bopp, Shaby, & Huser, 2020), and that the spatial dependence strength is often weakening as events become more extreme (see, e.g., Bacro, Gaetan, Opitz, & Toulemonde, 2020; Castro‐Camilo & Huser, 2020; Castro‐Camilo, Mhalla, & Opitz, 2020; Davison, Huser, & Thibaud, 2013; Huser, Opitz, & Thibaud, 2017; Huser & Wadsworth, 2020; Tawn, Shooter, Towe, & Lamb, 2018). In particular, under asymptotic independence , maxima become ultimately independent at the highest levels, requiring specialized models capturing the decay rate towards independence.…”

Section: Introductionmentioning

confidence: 99%

Max‐infinitely divisible models and inference for spatial extremes

Huser

Opitz

Thibaud

2020

Scandinavian J Statistics

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For many environmental processes, recent studies have shown that the dependence strength is decreasing when quantile levels increase. This implies that the popular max‐stable models are inadequate to capture the rate of joint tail decay, and to estimate joint extremal probabilities beyond observed levels. We here develop a more flexible modeling framework based on the class of max‐infinitely divisible processes, which extend max‐stable processes while retaining dependence properties that are natural for maxima. We propose two parametric constructions for max‐infinitely divisible models, which relax the max‐stability property but remain close to some popular max‐stable models obtained as special cases. The first model considers maxima over a finite, random number of independent observations, while the second model generalizes the spectral representation of max‐stable processes. Inference is performed using a pairwise likelihood. We illustrate the benefits of our new modeling framework on Dutch wind gust maxima calculated over different time units. Results strongly suggest that our proposed models outperform other natural models, such as the Student‐t copula process and its max‐stable limit, even for large block sizes.

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Section: Introductionmentioning

confidence: 99%

Max‐infinitely divisible models and inference for spatial extremes

Huser

Opitz

Thibaud

2020

Scandinavian J Statistics

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“…For computational convenience (and because of the constraints with INLA), we have assumed conditional independence of the data given the latent process. In cases where strong (tail) dependence prevails, more specialized extreme-value models should be considered, such as generalized Pareto processes (Thibaud and Opitz, 2015), max-stable models (Huser and Davison, 2014), and flexible copula models (Castro-Camilo and Huser, 2019). Although these models are attractive from a theoretical viewpoint, they are very cumbersome to fit, especially in high dimensions.…”

Section: Resultsmentioning

confidence: 99%

A Spliced Gamma-Generalized Pareto Model for Short-Term Extreme Wind Speed Probabilistic Forecasting

Castro‐Camilo

Huser

Rue

2019

JABES

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Renewable sources of energy such as wind power have become a sustainable alternative to fossil fuel-based energy. However, the uncertainty and fluctuation of the wind speed derived from its intermittent nature bring a great threat to the wind power production stability, and to the wind turbines themselves. Lately, much work has been done on developing models to forecast average wind speed values, yet surprisingly little has focused on proposing models to accurately forecast extreme wind speeds, which can damage the turbines. In this work, we develop a flexible spliced Gamma-Generalized Pareto model to forecast extreme and non-extreme wind speeds simultaneously. Our model belongs to the class of latent Gaussian models, for which inference is conveniently performed based on the integrated nested Laplace approximation method. Considering a flexible additive regression structure, we propose two models for the latent linear predictor to capture the spatio-temporal dynamics of wind speeds. Our models are fast to fit and can describe both the bulk and the tail of the wind speed distribution while producing short-term extreme and non-extreme wind speed probabilistic forecasts.

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“…However, this approach requires knowledge of relevant covariates, and asymptotically dependent max-stable models for spatial extremes have been shown to be too inflexible for many spatial datasets (Davison et al, 2013;Huser et al, 2017;Huser & Wadsworth, 2019;Wadsworth & Tawn, 2012). Another approach is to assume local stationarity for model fitting, see Blanchet and Creutin (2017) and Castro-Camilo and Huser (2019). This framework is well-suited to modeling processes with short-range dependence but is unlikely to fully capture dependence at large distances.…”

Section: Introductionmentioning

confidence: 99%

Spatial deformation for nonstationary extremal dependence

Richards

Wadsworth

2021

Environmetrics

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Modeling the extremal dependence structure of spatial data is considerably easier if that structure is stationary. However, for data observed over large or complicated domains, nonstationarity will often prevail. Current methods for modeling nonstationarity in extremal dependence rely on models that are either computationally difficult to fit or require prior knowledge of covariates.Sampson and Guttorp (1992) proposed a simple technique for handling nonstationarity in spatial dependence by smoothly mapping the sampling locations of the process from the original geographical space to a latent space where stationarity can be reasonably assumed. We present an extension of this method to a spatial extremes framework by considering least squares minimization of pairwise theoretical and empirical extremal dependence measures. Along with some practical advice on applying these deformations, we provide a detailed simulation study in which we propose three spatial processes with varying degrees of nonstationarity in their extremal and central dependence structures. The methodology is applied to Australian summer temperature extremes and UK precipitation to illustrate its efficacy compared with a naive modeling approach.

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Local Likelihood Estimation of Complex Tail Dependence Structures, Applied to U.S. Precipitation Extremes

Cited by 29 publications

References 59 publications

Max‐infinitely divisible models and inference for spatial extremes

Max‐infinitely divisible models and inference for spatial extremes

A Spliced Gamma-Generalized Pareto Model for Short-Term Extreme Wind Speed Probabilistic Forecasting

Spatial deformation for nonstationary extremal dependence

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