SUMMARY Conventional geostatistical methodology solves the problem of predicting realized value a linear functional Gaussian spatial stochastic process S(x) based on observations Yi = S(xi) + Zi at sampling locations xi, where are mutually independent, zero-mean random variables. We describe two applications for which distributional assumptions clearly inappropriate. The first concerns assessment residual contamination from nuclear weapons testing South Pacific island, in method generates...

We propose a multivariate extreme value threshold model for joint tail estimation which overcomes the problems encountered with existing techniques when variables are near independence. examine inference under and develop tests independence of extremes marginal variables, both thresholds fixed, they increase sample size. Motivated by results obtained from this model, we give new widely applicable characterisation dependence in includes models as special cases. A parameter governs form is...

Summary Multivariate extreme value theory and methods concern the characterization, estimation extrapolation of joint tail distribution a d-dimensional random variable. Existing approaches are based on limiting arguments in which all components variable become large at same rate. This limit approach is inappropriate when values variables unlikely to occur together or interest regions support where only subset extreme. In practice this restricts existing applications d typically 2 3. Under an...

This article presents a general framework for identifying and modeling the joint-tail distribution based on multivariate extreme value theories. We argue that approach is most efficient effective way to study events such as systemic risk crisis. show, using returns five major stock indices, use of traditional dependence measures could lead inaccurate portfolio assessment. explain how proposed here be exploited in number finance applications selection, management, Sharpe ratio targeting,...

Bivariate extreme value distributions arise as the limiting of renormalized componentwise maxima. No natural parametric family exists for dependence between marginal distributions, but there are considerable restrictions on structure. We consider modelling function with models, which two new models presented. Tests independence, and discriminating also given. The estimation procedure, flexibility illustrated an application to sea level data.

SUMMARY The classical treatment of multivariate extreme values is through componentwise ordering, though in practice most interest actual events. Here the point process observations which are at least one component considered. Parametric models for dependence between components must satisfy certain constraints. Two new techniques generating such presented. Aspects statistical estimation resulting discussed and illustrated with an application to oceanographic data.

Summary Standard approaches for modelling dependence within joint tail regions are based on extreme value methods which assume max-stability, a particular form of dependence. We develop models broader class structure provides natural link between max-stable and weaker forms including independence negative association. This approach overcomes many the problems that encountered with standard is basis Poisson process representation generalizes existing bivariate results. apply new techniques to...

SUMMARY Understanding and quantifying the behaviour of a rainfall process at extreme levels has important applications for design in civil engineering. As extremal analysis any environmental process, estimates often are required probability events that rarer than those already recorded. data on extremes scarce, all available sources information should be used inference. Consequently, research focused development techniques make optimal use data. I n this paper daily series is analysed within...

Journal Article A dependence measure for multivariate and spatial extreme values: Properties inference Get access Martin Schlather, Schlather Search other works by this author on: Oxford Academic Google Scholar Jonathan A. Tawn Biometrika, Volume 90, Issue 1, March 2003, Pages 139–156, https://doi.org/10.1093/biomet/90.1.139 Published: 01 2003

Multivariate extreme value distributions arise as the limiting joint distribution of normalized componentwise maxima/minima. No parametric family exists for dependence between margins. This paper extends to more than two variables models and results bivariate case obtained by Tawn (1988). Two new families physically motivated structure are presented illustrated with an application trivariate sea level data.

On coasts with high tidal ranges, or subject to surges, both still water levels and waves can be important in assessing flood risk; their relative importance depends on location the type of sea defence. The simultaneous occurrence large a level is therefore estimating combined effect defences. Wave period also run-up overtopping, so it useful have information joint distribution wave height period. Unless variables are either completely independent dependent, multivariate extremes difficult...

Current dependence models for spatial extremes are based upon max-stable processes. Within this class, there few inferentially viable available, and we propose one further model. More problematic the restrictive assumptions that must be made when using processes to model extremes: it assumed structure of observed is compatible with a limiting holds all events more extreme than those have already occurred. This problem has long been acknowledged in context finite-dimensional multivariate...

Summary Statistical methods for modelling extremes of stationary sequences have received much attention. The most common method is to model the rate and size exceedances some high constant threshold; modelled by using a generalized Pareto distribution. Frequently, data sets display non-stationarity; this especially in environmental applications. ozone set that presented here an example such set. Surface level levels complex seasonal patterns trends due mechanisms are involved formation....

Journal Article A sequential smoothing algorithm with linear computational cost Get access Paul Fearnhead, Fearnhead Department of Mathematics and Statistics, Lancaster University, LA1 4YFU.K.p.fearnhead@lancaster.ac.ukd.wyncoll@lancaster.ac.ukj.tawn@lancaster.ac.uk Search for other works by this author on: Oxford Academic Google Scholar David Wyncoll, Wyncoll Jonathan Tawn Biometrika, Volume 97, Issue 2, June 2010, Pages 447–464, https://doi.org/10.1093/biomet/asq013 Published: 01 2010...

Flooding is a natural phenomenon that regularly causes financial and human devastation around the world. In many countries risk of flooding managed by society through combination governmental agencies insurance industry. For both these types organisation an estimate largest, or most widespread, events can be expected to occur useful. Such estimates used help in preparing co‐ordinating flood mitigation activities re‐insurance industries assess risk. this paper we develop method simulate set...

Abstract To date, national‐ and regional‐scale flood risk assessments have provided valuable information about the annual expected consequences of flooding, but not exposure to widespread concurrent flooding that could damaging for people economy. We present a new method assessment accommodates flooding. It is based on statistical conditional exceedance model, which fitted gauged data describes joint probability extreme river flows or sea levels at multiple locations. The can be applied...

Max-stable processes arise as the only possible nontrivial limits for maxima of affinely normalized identically distributed stochastic processes, and thus form an important class models extreme values spatial processes. Until recently, inference max-stable has been restricted to use pairwise composite likelihoods, due intractability higher-dimensional distributions. In this work we consider random fields that are in domain attraction a widely used namely those constructed via manipulation...

Currently available models for spatial extremes suffer either from inflexibility in the dependence structures that they can capture, lack of scalability to high dimensions, or most cases, both these. We present an approach extreme value theory based on conditional multivariate model, whereby limit is formed through conditioning upon at a particular site being extreme. The ensuing methodology allows flexible class structures, as well be fitted dimensions. To overcome issues single site, we...

SUMMARY Risk assessment for many hydrological structures requires an estimate of the extremal behaviour rainfall regime within a specified catchment region. In most cases it is spatially aggregated which key process, though in practice only pointwise measurements from network sites over region are available. this paper we address problem making inferences about properties process data. Working usual extreme value paradigm, model derived resulting distribution determined by marginal tail and...