Statistics of Extremes: Challenges and Opportunities

Carvalho, Miguel de

doi:10.1002/9781118650318.ch9

Cited by 6 publications

(4 citation statements)

References 29 publications

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“…In the bivariate case, de Carvalho and proposed a non-parametric approach linking different spectral densities through exponential tilting. Castro et al (2015) extended this to covariate-dependent spectral densities; see also de Carvalho (2015). However, these methods are computationally intensive and difficult to apply in large dimensions.…”

Section: Introductionmentioning

confidence: 99%

Non-Stationary Dependence Structures for Spatial Extremes

Huser

Genton

2016

JABES

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Max-stable processes are natural models for spatial extremes because they provide suitable asymptotic approximations to the distribution of maxima of random fields. In the recent past, several parametric families of stationary max-stable models have been developed, and fitted to various types of data. However, a recurrent problem is the modeling of non-stationarity. In this paper, we develop non-stationary max-stable dependence structures in which covariates can be easily incorporated. Inference is performed using pairwise likelihoods, and its performance is assessed by an extensive simulation study based on a non-stationary locally isotropic extremal t model. Evidence that unknown parameters are well estimated is provided, and estimation of spatial return level curves is discussed. The methodology is demonstrated with temperature maxima recorded over a complex topography. Models are shown to satisfactorily capture extremal dependence.

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Section: Introductionmentioning

confidence: 99%

Non-Stationary Dependence Structures for Spatial Extremes

Huser

Genton

2016

JABES

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“…If H x (w) ≡ H x [0, w] is absolutely continuous, its conditional angular density is h x = dH x /dw. Further aspects of conditional angular measures are discussed in de Carvalho (2016).…”

Section: Conditional Modeling For Bivariate Extremesmentioning

confidence: 99%

“…Two related approaches to the current work are the so-called spectral density ratio model of de Carvalho and Davison (2014) and the spectral density regression model of Castro Camilo and de Carvalho (2016). While flexible, these approaches only apply to the setting where there are several pseudo-angles corresponding to the same value of the predictor-and thus they are inappropriate for our applied setting of interest.…”

Section: 3mentioning

confidence: 99%

Time-varying extreme value dependence with application to leading European stock markets

Castro‐Camilo¹,

Carvalho²,

Wadsworth³

2018

Ann. Appl. Stat.

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Extremal dependence between international stock markets is of particular interest in today's global financial landscape. However, previous studies have shown this dependence is not necessarily stationary over time. We concern ourselves with modeling extreme value dependence when that dependence is changing over time, or other suitable covariate. Working within a framework of asymptotic dependence, we introduce a regression model for the angular density of a bivariate extreme value distribution that allows us to assess how extremal dependence evolves over a covariate. We apply the proposed model to assess the dynamics governing extremal dependence of some leading European stock markets over the last three decades, and find evidence of an increase in extremal dependence over recent years.

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“…However, these approaches are limited to replicated one‐way ANOVA types of settings. de Carvalho () advocated the use of covariate‐adjusted angular densities, and Escobar‐Bach, Goegebeur, and Guillou () discussed estimation—in the bivariate and covariate‐dependent framework—of the Pickands dependence function based on local estimation with a minimum density power divergence criterion. Recently, Mhalla, Chavez‐demoulin, and Naveau () have constructed in a nonparametric framework smooth models for predictor‐dependent Pickands dependence functions based on generalized additive models, whereas Castro‐Camillo, de Carvalho, and Wadsworth () proposed nonparametric regression methods for predictor‐dependent angular measures; a key advantage of our method is that it can be used for modeling a high number (with limitation given by the sample size) of covariates of any type (from categorical to continuous), and it combines the flexibility of GAM along with a parametric specification to effectively learn about the dynamics governing the extremal dependence structure.…”

Section: Introductionmentioning

confidence: 99%

Regression‐type models for extremal dependence

Mhalla

Carvalho

Chavez‐Demoulin

2019

Scandinavian J Statistics

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We propose a vector generalized additive modeling framework for taking into account the effect of covariates on angular density functions in a multivariate extreme value context. The proposed methods are tailored for settings where the dependence between extreme values may change according to covariates. We devise a maximum penalized log‐likelihood estimator, discuss details of the estimation procedure, and derive its consistency and asymptotic normality. The simulation study suggests that the proposed methods perform well in a wealth of simulation scenarios by accurately recovering the true covariate‐adjusted angular density. Our empirical analysis reveals relevant dynamics of the dependence between extreme air temperatures in two alpine resorts during the winter season.

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Statistics of Extremes: Challenges and Opportunities

Abstract: In this chapter I provide a personal view on some recent concepts and methods of statistics of extremes, and I discuss challenges and opportunities which could lead to potential future developments.

Cited by 6 publications

References 29 publications

Non-Stationary Dependence Structures for Spatial Extremes

Non-Stationary Dependence Structures for Spatial Extremes

Time-varying extreme value dependence with application to leading European stock markets

Regression‐type models for extremal dependence

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