Nonparametric Analysis of Temporal Trend When Fitting Parametric Models to Extreme­Value Data

Hall, Peter; Tajvidi, Nader

doi:10.1214/ss/1009212755

Cited by 128 publications

(16 citation statements)

References 23 publications

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“…In many applications, it would be necessary to take semi-parametric formulations for dependence on x, but as we have data at relatively few sites, we use parametric forms. Davison & Ramesh (2000), Hall & Tajvidi (2000), Pauli & Coles (2001), Chavez-Demoulin & Davison (2005 and Padoan & Wand (2008) describe approaches to more flexible modelling, applied by Ramesh & Davison (2002) and Butler et al (2007).…”

Section: (B) Datamentioning

confidence: 99%

Geostatistics of extremes

2011

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We describe a prototype approach to flexible modelling for maxima observed at sites in a spatial domain, based on fitting of max-stable processes derived from underlying Gaussian random fields. The models we propose have generalized extreme-value marginal distributions throughout the spatial domain, consistent with statistical theory for maxima in simpler cases, and can incorporate both geostatistical correlation functions and random set components. Parameter estimation and fitting are performed through composite likelihood inference applied to observations from pairs of sites, with occurrence times of maxima taken into account if desired, and competing models are compared using appropriate information criteria. Diagnostics for lack of model fit are based on maxima from groups of sites. The approach is illustrated using annual maximum temperatures in Switzerland, with risk analysis proposed using simulations from the fitted max-stable model. Drawbacks and possible developments of the approach are discussed.

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Section: (B) Datamentioning

confidence: 99%

Geostatistics of extremes

2011

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“…To simplify likelihood calculations, which become complicated in the presence of missing data, a latent variable representation of the bivariate logistic distribution can be exploited within a Markov chain Monte Carlo setup for the model (Tawn 1990). Spatial smoothing on model parameters can also be incorporated as part of the modelling via a range of local smoothing approaches which have been developed for extreme values (Davison & Ramesh 1998;Hall & Tajvidi 2000). We propose, in particular, to use dynamic representatives of non-Gaussian filters, estimating marginal and dependence parameters simultaneously so that all sources of parameter estimation are accounted for in predictive return level calculations.…”

Section: Spatial Modellingmentioning

confidence: 99%

Bayesian modelling of extreme surges on the UK east coast

Coles

Tawn

2005

Phil. Trans. R. Soc. A.

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The catastrophic surge event of 1953 on the eastern UK and northern European coastlines led to widespread agreement on the necessity of a coordinated response to understand the risk of future oceanographic flood events and, so far as possible, to afford protection against such events. One element of this response was better use of historical data and scientific knowledge in assessing flood risk. The timing of the event also coincided roughly with the birth of extreme value theory as a statistical discipline for measuring risks of extreme events, and over the last 50 years, as techniques have been developed and refined, various attempts have been made to improve the precision of flood risk assessment around the UK coastline. In part, this article provides a review of such developments. Our broader aim, however, is to show how modern statistical modelling techniques, allied with the tools of extreme value theory and knowledge of sea-dynamic physics, can lead to further improvements in flood risk assessment. Our long-term goal is a coherent spatial model that exploits spatial smoothness in the surge process characteristics and we outline the details of such a model. The analysis of the present article, however, is restricted to a site-by-site analysis of high-tide surges. Nonetheless, we argue that the Bayesian methodology adopted for such analysis enables a risk-based interpretation of results that is most natural in this setting, and preferable to inferences that are available from more conventional analyses.

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“…First, one may model the trend in the parameters of such models as a specific functional of the covariates; see, for example, Smith (1989) for the GEV model and Davison and Smith (1990) for the GPD model. Second, the trend can also be nonparametrically estimated using various local estimation techniques; see, for example, Davison and Ramesh (2000) using the local likelihood method, Hall and Tajvidi (2000) using the local linearization method, among others. Compared to all these studies, we do not impose a fully parameterized model and therefore maintain a semiparametric approach.…”

Section: Introductionmentioning

confidence: 99%

Trends in Extreme Value Indices

Haan

Zhou

2020

Journal of the American Statistical Association

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We consider extreme value analysis for independent but nonidentically distributed observations. In particular, the observations do not share the same extreme value index. Assuming continuously changing extreme value indices, we provide a nonparametric estimate for the functional extreme value index. Besides estimating the extreme value index locally, we also provide a global estimator for the trend and its joint asymptotic theory. The asymptotic theory for the global estimator can be used for testing a prespecified parametric trend in the extreme value indices. In particular, it can be applied to test whether the extreme value index remains at a constant level across all observations.

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Nonparametric Analysis of Temporal Trend When Fitting Parametric Models to ExtremeValue Data

Cited by 128 publications

References 23 publications

Geostatistics of extremes

Geostatistics of extremes

Bayesian modelling of extreme surges on the UK east coast

Trends in Extreme Value Indices

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Nonparametric Analysis of Temporal Trend When Fitting Parametric Models to Extreme­Value Data

Cited by 128 publications

References 23 publications

Geostatistics of extremes

Geostatistics of extremes

Bayesian modelling of extreme surges on the UK east coast

Trends in Extreme Value Indices

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Product

Resources

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Nonparametric Analysis of Temporal Trend When Fitting Parametric Models to ExtremeValue Data