probabilities of concurrent extremes the statistical modelling of spatial extremes has recently made major advances much of its focus so far has been on the modelling of the magnitudes of extreme events but little attention has been paid on the timing of extremes to address this gap this paper introduces the notion of extremal concurrence suppose that one measures precipitation at several synoptic stations over multiple days we say that extremes are concurrent if the maximum precipitation over time at each station is achieved simultaneously e g on a single day under general conditions we show that the finite sample concurrence probability converges to an asymptotic quantity deemed extremal concurrence probability using palm calculus we establish general expressions for the extremal concurrence probability through the max stable process emerging in the limit of the componentwise maxima of the sample explicit forms of the extremal concurrence probabilities are obtained for various max stable models and several estimators are introduced in particular we prove that the pairwise extremal concurrence probability for max stable vectors is precisely equal to the kendall s tau the estimators are evaluated by using simulations and applied to study the concurrence patterns of temperature extremes in the united states the results demonstrate that concurrence probability can provide a powerful new perspective and tools for the analysis of the spatial structure and impact of extremes

extremal behaviour of aggregated data with an application to downscaling summary the distribution of spatially aggregated data from a stochastic process x may exhibit tail behaviour different from that of its marginal distributions for a large class of aggregating functionals ell we introduce the ell extremal coefficient which quantifies this difference as a function of the extremal spatial dependence in x we also obtain the joint extremal dependence for multiple aggregation functionals applied to the same process formulae for the ell extremal coefficients and multivariate dependence structures are derived in important special cases the results provide a theoretical link between the extremal distribution of the aggregated data and the corresponding underlying process which we exploit to develop a method for statistical downscaling we apply our framework to downscale daily temperature maxima in the south of france from a gridded dataset and use our model to generate high resolution maps of the warmest day during the 2003 heatwave

modelling dependence within joint tail regions standard approaches for modelling dependence within joint tail regions are based on extreme value methods which assume max stability a particular form of joint tail dependence we develop joint tail models based on a broader class of dependence structure which provides a natural link between max stable models and weaker forms of dependence including independence and negative association this approach overcomes many of the problems that are encountered with standard methods and is the basis for a poisson process representation that generalizes existing bivariate results we apply the new techniques to simulated and environmental data and demonstrate the marked advantage that the new approach offers for joint tail extrapolation

transient analysis of viscoelastic helical rods subject to time dependent loads abstract the transient analysis of viscoelastic helical rods subject to time dependent loads are examined in the laplace domain the governing equations for naturally twisted and curved spatial rods obtained using the timoshenko beam theory are rewritten for cylindrical helical rods the curvature of the rod axis effect of rotary inertia and shear and axial deformations are considered in the formulation the material of the rod is assumed to be homogeneous isotropic and linear viscoelastic the viscoelastic constitutive equations are written in the boltzmann volterra form ordinary differential equations in canonical form obtained in the laplace domain are solved numerically using the complementary functions method to calculate the dynamic stiffness matrix of the problem the solutions obtained are transformed to the real space using an appropriate numerical inverse laplace transform method numerical results for quasi static and dynamic response of viscoelastic models are presented in the form of graphics

modelling extreme multivariate events summary the classical treatment of multivariate extreme values is through componentwise ordering though in practice most interest is in actual extreme events here the point process of observations which are extreme in at least one component is considered parametric models for the dependence between components must satisfy certain constraints two new techniques for generating such models are presented aspects of the statistical estimation of the resulting models are discussed and are illustrated with an application to oceanographic data

generalized additive models for exceedances of high thresholds with an application to return level estimation for u s wind gusts generalized additive model gam forms offer a flexible approach to capturing marginal variation such forms are used here to represent distributional variation in extreme values and presented in t

max infinitely divisible and max stable sample continuous processes conditions for a process on a compact metric spaces to be simultaneously max infinitely divisible and sample continuous are obtained although they fall short of a complete characterization of such processes these conditions yield complete descriptions of the sample continuous non degenerate max stable processes ons and of the infinitely divisible non void random compact subsets of a banach space under the operation of convex hull of unions

markov chain models for threshold exceedances in recent research on extreme value statistics there has been an extensive development of threshold methods first in the univariate case and subsequently in the multivariate case as well in this paper an alternative methodology for extreme values of univariate time series is developed by assuming that the time series is markovian and using bivariate extreme value theory to suggest appropriate models for the transition distributions a new likelihood representation for threshold methods is presented which we apply to a markovian time series an important motivation for developing this kind of theory is the possibility of calculating probability distributions for functionals of extreme events we address this issue by showing how a theory of compound poisson limits for additive functionals can be combined with simulation to obtain numerical solutions for problems of practical interest the methods are illustrated by application to temperature data

stationary min stable stochastic processes we consider the class of stationary stochastic processes whose margins are jointly min stable we show how the scalar elements can be generated by a single realization of a standard homogeneous poisson process on the upper half strip 0 1 x r and a group of l1 isometries we include a dobrushin like result for the realizations in continuous time

dependence modelling for spatial extremes current dependence models for spatial extremes are based upon max stable processes within this class there are few inferentially viable models available and we propose one further model more problematic are the restrictive assumptions that must be made when using max stable processes to model dependence for spatial extremes it must be assumed that the dependence structure of the observed extremes is compatible with a limiting model that holds for all events more extreme than those that have already occurred this problem has long been acknowledged in the context of finite dimensional multivariate extremes in particular when data display dependence at observable levels but are independent in the limit we propose a flexible class of models that is suitable for such data in a spatial context in addition we consider the situation where the extremal dependence structure may vary with distance we apply our models to spatially referenced significant wave height data from the north sea finding evidence that their extremal structure is not compatible with a limiting dependence model

conditional simulation of max stable processes summary since many environmental processes such as heat waves or precipitation are spatial in extent it is likely that a single extreme event affects several loca tions and the areal modelling of extremes is therefore essential if the spatial dependence of e xtremes has to be appropriately taken into account this paper proposes a framework for conditional simulations of max stable processes and give closed forms for brown resnick and schlather processes we test the method on simulated data and give an application to extreme rainfall around zurich and extreme temperature in switzerland results show that the proposed framework provides accurate conditional simulations and can handle real sized problems

exact simulation of max stable processes max stable processes play an important role as models for spatial extreme events their complex structure as the pointwise maximum over an infinite number of random functions makes their simulation difficult algorithms based on finite approximations are often inexact and computationally inefficient we present a new algorithm for exact simulation of a max stable process at a finite number of locations it relies on the idea of simulating only the extremal functions that is those functions in the construction of a max stable process that effectively contribute to the pointwise maximum we further generalize the algorithm by dieker mikosch 2015 for brown resnick processes and use it for exact simulation via the spectral measure we study the complexity of both algorithms prove that our new approach via extremal functions is always more efficient and provide closed form expressions for their implementation that cover most popular models for max stable processes and multivariate extreme value distributions for simulation on dense grids an adaptive design of the extremal function algorithm is proposed

a new class of models for bivariate joint tails summary a fundamental issue in applied multivariate extreme value analysis is modelling dependence within joint tail regions the primary focus of this work is to extend the classical pseudopolar treatment of multivariate extremes to develop an asymptotically motivated representation of extremal dependence that also encompasses asymptotic independence starting with the usual mild bivariate regular variation assumptions that underpin the coefficient of tail dependence as a measure of extremal dependence our main result is a characterization of the limiting structure of the joint survivor function in terms of an essentially arbitrary non negative measure that must satisfy some mild constraints we then construct parametric models from this new class and study in detail one example that accommodates asymptotic dependence asymptotic independence and asymmetry within a straightforward parsimonious parameterization we provide a fast simulation algorithm for this example and detail likelihood based inference including tests for asymptotic dependence and symmetry which are useful for submodel selection we illustrate this model by application to both simulated and real data in contrast with the classical multivariate extreme value approach which concentrates on the limiting distribution of normalized componentwise maxima our framework focuses directly on the structure of the limiting joint survivor function and provides significant extensions of both the theoretical and the practical tools that are available for joint tail modelling

dynamic analysis of linear viscoelastic cylindrical and conical helicoidal rods using the mixed fem abstract the objective of this study is to investigate the influence of the rotary inertia on dynamic behavior of linear viscoelastic cylindrical and conical helixes by means of the laplace transform mixed finite element formulation and solution the element matrix is based on the timoshenko beam theory the influence of rotary inertias is considered in the dynamic analysis which is original in the literature rectangular sine and step type of impulsive loads are applied on helices having rectangular cross sections with various aspect ratios the kelvin and standard models are used for defining the linear viscoelastic material behavior and by means of the correspondence principle the elastic viscoelastic analogy the material parameters are replaced with their complex counterparts in the laplace domain the analysis is carried out in the laplace domain and the results are transformed back to time space numerically by modified durbin s algorithm first the solution algorithm is verified using the existing open sources in the literature and afterwards some benchmark examples such as conical viscoelastic rods are handled

modelling across extremal dependence classes different dependence scenarios can arise in multivariate extremes entailing careful selection of an appropriate class of models in bivariate extremes the variables are either asymptotically dependent or are asymptotically independent most available statistical models suit one or other of these cases but not both resulting in a stage in the inference that is unaccounted for but can substantially impact subsequent extrapolation existing modelling solutions to this problem are either applicable only on sub domains or appeal to multiple limit theories we introduce a unified representation for bivariate extremes that encompasses a wide variety of dependence scenarios and applies when at least one variable is large our representation motivates a parametric model that encompasses both dependence classes we implement a simple version of this model and show that it performs well in a range of settings

an echolocation model for range discrimination of multiple closely spaced objects transformation of spectrogram into the reflected intensity distribution using frequency modulated echolocation bats can discriminate the range of objects with an accuracy of less than a millimeter however bats echolocation mechanism is not well understood the delay separation of three or more closely spaced objects can be determined through analysis of the echo spectrum however delay times cannot be properly correlated with objects using only the echo spectrum because the sequence of delay separations cannot be determined without information on temporal changes in the interference pattern of the echoes to illustrate this gaussian chirplets with a carrier frequency compatible with bat emission sweep rates were used the delay time for object 1 t1 can be estimated from the echo spectrum around the onset time the delay time for object 2 is obtained by adding t1 to the delay separation between objects 1 and 2 extracted from the first appearance of interference effects further objects can be located in sequence by this same procedure this model can determine delay times for three or more closely spaced objects with an accuracy of about 1 micros when all the objects are located within 30 micros of delay separation this model is applicable for the range discrimination of objects having different reflected intensities and in a noisy environment 0 db signal to noise ratio while the cross correlation method is hard to apply to these problems

bayesian modeling of air pollution extremes using nested multivariate max stable processes capturing the potentially strong dependence among the peak concentrations of multiple air pollutants across a spatial region is crucial for assessing the related public health risks in order to investigate the multivariate spatial dependence properties of air pollution extremes we introduce a new class of multivariate max stable processes our proposed model admits a hierarchical tree based formulation in which the data are conditionally independent given some latent nested positive stable random factors the hierarchical structure facilitates bayesian inference and offers a convenient and interpretable characterization we fit this nested multivariate max stable model to the maxima of air pollution concentrations and temperatures recorded at a number of sites in the los angeles area showing that the proposed model succeeds in capturing their complex tail dependence structure

an echolocation model for the restoration of an acoustic image from a single emission echo bats can form a fine acoustic image of an object using frequency modulated echolocation sound the acoustic image is an impulse response known as a reflected intensity distribution which is composed of amplitude and phase spectra over a range of frequencies however bats detect only the amplitude spectrum due to the low time resolution of their peripheral auditory system and the frequency range of emission is restricted it is therefore necessary to restore the acoustic image from limited information the amplitude spectrum varies with the changes in the configuration of the reflected intensity distribution while the phase spectrum varies with the changes in its configuration and location here by introducing some reasonable constraints a method is proposed for restoring an acoustic image from the echo the configuration is extrapolated from the amplitude spectrum of the restricted frequency range by using the continuity condition of the amplitude spectrum at the minimum frequency of the emission and the minimum phase condition the determination of the location requires extracting the amplitude spectra which vary with its location for this purpose the gaussian chirplets with a carrier frequency compatible with bat emission sweep rates were used the location is estimated from the temporal changes of the amplitude spectra

methods of interconversion between linear viscoelastic material functions part ii an approximate analytical method abstract a new very simple approximate interconversion method is proposed and verified by examples this technique employing the slope of the source function on logarithmic scales is found to substantially enhance the accuracy compared to existing approximate methods the new method is based on the characteristic mathematical properties of the narrow band weight functions involved in the interrelationships between broad band material functions with the material functions represented locally by a power law they are interrelated in terms of adjustment factors expressed through the local log log slope of the given source function a number of existing approximate interconversion methods are also tested and compared with the new method in part i park and schapery 1998 an efficient numerical interconversion method based on a prony exponential series representation of both the source and target functions was presented such a series representation is not needed here the new method when applied to the prediction of broad band time dependent functions from laplace or fourier transforms is an approximate method of transform inversion that is applicable to functions which are not necessarily viscoelastic material functions

modeling spatial extremes via ensemble of trees of pairwise copulas assessing the risk of extreme events in a spatial domain such as hurricanes floods and droughts presents a unique significance in practice unfortunately the existing extreme value statistical models are typically not feasible for practical large scale problems graphical models on the other hand are capable of handling sizable number of variables but have yet to be explored in the realm of extreme value analysis to bridge the gap an extreme value graphical model is introduced in this paper i e an ensemble of trees of pairwise copulas etpc in the proposed graphical model extreme value marginal distributions are stitched together by means of a pairwise copulas which in turn are the building blocks of the ensemble of trees novel linear complexity stochastic gradient based algorithms are then developed for learning the etpc model and inferring missing data as a result the etpc model is applicable to extreme value problems with thousands of variables it can be proven that under mild conditions the etpc model exhibits the favorable property of tail dependence between an arbitrary pair of sites variables consequently the model is able to reliably capture statistical dependence between extreme values at different sites experimental results for both synthetic and real data demonstrate the advantages of the etpc model in modeling fitting imputation and computational efficiency

a construction principle for multivariate extreme value distributions we present a construction principle for the spectral density of a multivariate extreme value distribution it generalizes the pairwise beta model introduced in the literature recently and may be used to obtain new parametric models from lower dimensional spectral densities we illustrate the flexibility of this new class of models and apply it to a wind speed dataset

bivariate extreme value theory models and estimation summary bivariate extreme value distributions arise as the limiting distributions of renormalized componentwise maxima no natural parametric family exists for the dependence between the marginal distributions but there are considerable restrictions on the dependence structure we consider modelling the dependence function with parametric models for which two new models are presented tests for independence and discriminating between models are also given the estimation procedure and the flexibility of the new models are illustrated with an application to sea level data extreme value theory has recently been an area of much theoretical and practical work univariate theory is a well documented area whereas bivariate multivariate extreme value theory has until recently received surprisingly little attention in the multivariate case no natural parametric family exists for the dependence structure so this must be modelled in some way in the analysis of environmental extreme value data there is a need for models of dependence between extremes from different sources for example at various sea ports or at various points of a river in this paper we consider bivariate extreme value distributions we assume without loss of generality that we have exponential marginal distributions with unit means the class of bivariate exponential distributions in which we are interested satisfy a strong stability relation exponential variables x y satisfy the stability relation if and only if w min ax by is also exponentially distributed for all a b 0 pickands 1981 therefore the models we will consider have particular application in reliability and survival analysis one approach to modelling the dependence structure is via parametric models this requires a flexible family of models which satisfy certain constraints models are of two kinds either differentiable or nondifferentiable all nondifferentiable models give distri butions which are singular with nonzero probability concentrated on a certain subspace the differentiable models have densities but the existing models are symmetric which leads to the variables being exchangeable here we present two new asymmetric differenti able models which have increased flexibility properties of the differentiable models are examined estimation of the parametric models has previously been by ad hoc methods because there is a nonregular estimation problem when the margins are independent for the

association models for a multivariate binary response models for a multivariate binary response are parameterized by univariate marginal probabilities and dependence ratios of all orders the w order dependence ratio is the joint success probability of w binary responses divided by the joint success probability assuming independence this parameterization supports likelihood based inference for both regression parameters relating marginal probabilities to explanatory variables and association model parameters relating dependence ratios to simple and meaningful mechanisms five types of association models are proposed where responses are 1 independent given a necessary factor for the possibility of a success 2 independent given a latent binary factor 3 independent given a latent beta distributed variable 4 follow a markov chain and 5 follow one of two first order markov chains depending on the realization of a binary latent factor these models are illustrated by reanalyzing three data sets foremost a set of binary time series on auranofin therapy against arthritis likelihood based approaches are contrasted with approaches based on generalized estimating equations association models specified by dependence ratios are contrasted with other models for a multivariate binary response that are specified by odds ratios or correlation coefficients

statistics for near independence in multivariate extreme values we propose a multivariate extreme value threshold model for joint tail estimation which overcomes the problems encountered with existing techniques when the variables are near independence we examine inference under the model and develop tests for independence of extremes of the marginal variables both when the thresholds are fixed and when they increase with the sample size motivated by results obtained from this model we give a new and widely applicable characterisation of dependence in the joint tail which includes existing models as special cases a new parameter which governs the form of dependence is of fundamental importance to this characterisation by estimating this parameter we develop a diagnostic test which assesses the applicability of bivariate extreme value joint tail models the methods are demonstrated through simulation and by analysing two previously published data sets

on convergence toward an extreme value distribution in c 0 1 the structure of extreme value distributions in infinite dimensional space is well known we characterize the domain of attraction of such extreme value distributions in the framework of gine hahn and vatan we intend to use the result for statistical applications

a note on composite likelihood inference and model selection a composite likelihood consists of a combination of valid likelihood objects usually related to small subsets of data the merit of composite likelihood is to reduce the computational complexity so that it is possible to deal with large datasets and very complex models even when the use of standard likelihood or bayesian methods is not feasible in this paper we aim to suggest an integrated general approach to inference and model selection using composite likelihood methods in particular we introduce an information criterion for model selection based on composite likelihood we also describe applications to the modelling of time series of counts through dynamic generalised linear models and to the analysis of the well known old faithful geyser dataset

the normal law under linear restrictions simulation and estimation via minimax tilting summary simulation from the truncated multivariate normal distribution in high dimensions is a recurrent problem in statistical computing and is typically only feasible by using approximate markov chain monte carlo sampling we propose a minimax tilting method for exact independently and identically distributed data simulation from the truncated multivariate normal distribution the new methodology provides both a method for simulation and an efficient estimator to hitherto intractable gaussian integrals we prove that the estimator has a rare vanishing relative error asymptotic property numerical experiments suggest that the scheme proposed is accurate in a wide range of set ups for which competing estimation schemes fail we give an application to exact independently and identically distributed data simulation from the bayesian posterior of the probit regression model

space time modelling of extreme events max stable processes are the natural analogues of the generalized extreme value distribution when modelling extreme events in space and time under suitable conditions these processes are asymptotically justified models for maxima of independent replications of random fields and they are also suitable for the modelling of extreme measurements over high thresholds this paper shows how a pairwise censored likelihood can be used for consistent estimation of the extremes of space time data under mild mixing conditions and illustrates this by fitting an extension of a model of schlather 2002 to hourly rainfall data a block bootstrap procedure is used for uncertainty assessment estimator efficiency is considered and the choice of pairs to be included in the pairwise likelihood is discussed the proposed model fits the data better than some natural competitors

regional modelling of extreme storms via max stable processes asymptotic models for extremes of random processes often form the basis for estimating the extremal behaviour of environmental phenomena most such phenomena have a spatial dimension and the aim of this paper is to develop a procedure for modelling in continuous space the spatial dependence within extreme events a principal objective in the analysis as with other current research on extremes is to base inference on as much of the available data as possible the modelling procedures are justified on simulated data and subsequently applied to a series of rainfall data

local likelihood estimation of complex tail dependence structures applied to u s precipitation extremes to disentangle the complex nonstationary dependence structure of precipitation extremes over the entire contiguous united states u s we propose a flexible local approach based on factor copula

spatial extremes models for the stationary case the aim of this paper is to provide models for spatial extremes in the case of stationarity the spatial dependence at extreme levels of a stationary process is modeled using an extension of the theory of max stable processes of de haan and pickands probab theory related fields 72 1986 477 492 we propose three one dimensional and three two dimensional models these models depend on just one parameter or a few parameters that measure the strength of tail dependence as a function of the distance between locations we also propose two estimators for this parameter and prove consistency under domain of attraction conditions and asymptotic normality under appropriate extra conditions

ergodic properties of sum and max stable stationary random fields via null and positive group actions we establish characterization results for the ergodicity of sym metric stable ss and frechet max stable stationary random fields we first show that the result of samorodnitsky 35 remains valid in the multiparameter setting i e a stationary ss 0 2 random field is ergodic or equivalently weakly mixing if and only if it is generated by a null group action the similarity of the spectral representations for sum and max stable random fields yields paral lel characterization results in the max stable setting by establishing multiparameter versions of stochastic and birkhoff ergodic theorems we give a criterion for ergodicity of these random fields which is valid for all dimensions and new even in the one dimensional case we also prove the equivalence of ergodicity and weak mixing for the general class of positively dependent random fields ams 2000 subject classifications primary 60g10 60g52 60g60 secondary 37a40 37a50

multivariate max stable spatial processes summary max stable processes allow the spatial dependence of extremes to be modelled and quantified so they are widely adopted in applications for a better understanding of extremes it may be useful to study several variables simultaneously to this end we study the maxima of independent replicates of multivariate processes both in the gaussian and student t cases we define a poisson process construction and introduce multivariate versions of the smith gaussian extreme value the schlather extremal gaussian and extremal t and the brown resnick models we develop inference for the models based on composite likelihoods we present results of monte carlo simulations and an application to daily maximum wind speed and wind gust

an m estimator of spatial tail dependence tail dependence models for distributions attracted to a max stable law are tted using observations above a high threshold to cope with spatial high dimensional data a rank based m estimator is proposed relying on bivariate margins only a data driven weight matrix is used to minimize the asymptotic variance empirical process arguments show that the estimator is consistent and asymptotically normal its nite sample performance is assessed in simulation experiments involving popular max stable processes perturbed with additive noise an analysis of wind speed data from the netherlands illustrates the method

asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions abstract large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described specifically the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived these results generalize the work of moran 1971 chant 1974 and chernoff 1954 some of chant s results are shown to be incorrect the approach used in deriving these results follows from comments made by moran and chant the problem is shown to be asymptotically equivalent to the problem of estimating the restricted mean of a multivariate gaussian distribution from a sample of size 1 in this representation the gaussian random variable corresponds to the limit of the normalized score statistic and the estimate of the mean corresponds to the limit of the normalized maximum likelihood estimator thus the limiting distribution of the maximum likelihood estimator is the same as the distribution of the projection of the gaussian random v

peaks over thresholds modeling with multivariate generalized pareto distributions when assessing the impact of extreme events it is often not just a single component but the combined behavior of several components which is important statistical modeling using multivariate gen

models and inference for uncertainty in extremal dependence conventionally modelling of multivariate extremes has been based on the class of multivariate extreme value distributions more recently other classes have been developed allowing for the possibility that whilst dependence is observed at finite levels the limit distribution is independent a number of articles have shown this development to be important for accurate estimation of the extremal properties both of theoretical processes and observed datasets it has also been shown that so far as dependence is concerned the choice between modelling with either asymptotically dependent or asymptotically independent distributions can be far more influential than model choice within either of these two classes in this paper we explore the issue of modelling across both classes examining in particular the effect of uncertainty caused by lack of knowledge about the status of asymptotic dependence this is achieved by new multivariate models whose parameter spaces are such that asymptotic dependence occurs on a boundary standard techniques in bayesian inference implemented through markov chain monte carlo enable inferences to be drawn that assign posterior probability mass to the boundary region the techniques are illustrated on a set of oceanographic data for which previous analyses have shown that it is difficult to resolve the question of asymptotic dependence status which is however important in model extrapolation

modeling spatial processes with unknown extremal dependence class abstractmany environmental processes exhibit weakening spatial dependence as events become more extreme well known limiting models such as max stable or generalized pareto processes cannot capture this which can lead to a preference for models that exhibit a property known as asymptotic independence however weakening dependence does not automatically imply asymptotic independence and whether the process is truly asymptotically in dependent is usually far from clear the distinction is key as it can have a large impact upon extrapolation that is the estimated probabilities of events more extreme than those observed in this work we present a single spatial model that is able to capture both dependence classes in a parsimonious manner and with a smooth transition between the two cases the model covers a wide range of possibilities from asymptotic independence through to complete dependence and permits weakening dependence of extremes even under asymptotic dependence censored likelihood based

ordered multivariate extremes multivariate extreme value models and associated statistical methods are developed for vector observations whose components are subject to an order restriction the approach extends the multivariate threshold methodology of coles and tawn joe and co workers and smith and co workers the results are illustrated by an analysis of extreme rainfalls of different durations and by a study of the problem of linking a long series of daily rainfall extremes with a partially overlapping shorter series of hourly extremes

marginal regression analysis of a multivariate binary response we propose the use of the mean parameter for regression analysis of a multivariate binary response we model the association using dependence ratios defined in terms of the mean parameter the components of which are the joint success probabilities of all orders this permits flexible modelling of higher order associations using maximum likelihood estimation we reanalyse two data sets one with variable cluster size and the other a longitudinal data set with constant cluster size

mapping extreme snowfalls in the french alps using max stable processes 1 the evaluation of extreme snowfalls is an important challenge for hazard management in mountainous regions in this paper the extreme snowfall data acquired from 40 meteorological stations in the french alps since 1966 are analyzed using spatial extreme statistics they are then modeled within the formal framework of max stable processes msps which are the generalization of the univariate extreme value theory to the spatial multivariate case the three main msps now available are compared using composite likelihood maximization and the most flexible brown resnick one is retained on the basis of the takeuchi information criterion taking into account anisotropy by space transformation furthermore different models with smooth trends linear and splines for the spatial evolution of the generalized extreme value gev parameters are tested to allow snowfall maps for different return periods to be produced after altitudinal correction that separates spatial and orographic effects the different spatial models are fitted to the data within the max stable framework allowing inference of the gev margins and the extremal dependence simultaneously finally a nested model selection procedure is employed to select the best linear and spline models results show that the best linear model produces reasonable quantile maps assessed by cross validation using other stations but it is outperformed by the best spline model which better captures the complex evolution of gev parameters with space for a given return period and at fixed elevation of 2000 m extreme 3 day snowfalls are higher in the ne and se of the french alps maxima of the location parameter of the gev margins are located in the north and south while maxima of the scale parameter are located in the se which corresponds to the mediterranean influence that tends to bring more variability besides the dependence of extreme snowfalls is shown to be stronger on the local orientation of the alps an important result for meteorological variables confirming previous studies computations are performed for different accumulation durations which enable obtaining magnitude frequency curves and show that the intensity of the extremal directional dependence effect is all the more important when the duration is short finally we show how the fitted model can be used to evaluate joint exceedence probabilities and conditional return level maps which can be useful for operational risk management

composite likelihood estimation for the brown resnick process summary genton et al 2011 investigated the gain in efficiency when triplewise rather than pairwise likelihood is used to fit the popular smith max stable model for spatial extremes we generalize their results to the brown resnick model and show that the efficiency gain is substantial only for very smooth processes which are generally unrealistic in applications

almost sure continuity of stable moving average processes with index less than one rootzen 1978 a donne une condition suffisante pour la continuite d echantillon des processus a moyenne mobile relativement au mouvement stable d indice inferieur a deux on donne une preuve simple de ce critere pour 1 et on montre que la condition est alors aussi necessaire pour la continuite du processus

modelling multivariate extreme value distributions summary multivariate extreme value distributions arise as the limiting joint distribution of normalized componentwise maxima minima no parametric family exists for the depen dence between the margins this paper extends to more than two variables the models and results for the bivariate case obtained by tawn 1988 two new families of physically motivated parametric models for the dependence structure are presented and are illus trated with an application to trivariate extreme sea level data in the analysis of environmental extreme value data there is often need to study joint inter site extreme behaviour examples are joint flooding at various sea ports or at various rain gauges in this paper the class of multivariate extreme value distributions is considered the marginal distributions are all extreme value distributions without loss of generality we follow pickands s 1981 approach in transforming the margins to unit mean exponential distributions the resulting class of p variable multivariate exponential distributions satisfies a strong stability relation de haan resnick 1977 and pickands 1981 show that the resulting dependence structure is uniquely specified up to an arbitrary finite positive measure on p 1 variables therefore the bivariate dependence structure is univariate only when p 3 as considered here does the problem become really multivari ate in addition unlike in the multivariate normal distribution the multivariate depen dence structure is generally only restricted and not uniquely specified by the dependence structure of all possible pairs much has been written about the representations of multivariate extremes see resnick 1987 for a good review on the other hand models and estimation for such distributions have received little attention these aspects are considered here as no finite parametric family exists for the general dependence structure it must be modelled in some way thus true multivariate models are required using the most flexible bivariate model of tawn 1988 as a basis multivariate extensions are generated a model derived in the discrete choice literature will also be introduced and extended the resulting families of models are physically motivated flexible and possess hierarchical properties

modelling extremes of the areal rainfall process risk assessment for many hydrological structures requires an estimate of the extremal behaviour of the rainfall regime within a specified catchment region in most cases it is the spatially aggregated rainfall which is the key process though in practice only pointwise rainfall measurements from a network of sites over the region are available in this paper we address the problem of making inferences about the extremal properties of the aggregated process from the pointwise data working within the usual extreme value paradigm a model is derived in which the resulting distribution is determined by the marginal tail behaviour and spatial dependence at extreme levels of the process data collected from a region in the south west of england are used to illustrate the procedure

a weibull model for dependent censoring a bivariate weibull model is proposed for censored survival data when there may be dependence between the survival and censoring random variables the model is based on marginal transformations of the pickands class of bivariate exponential distributions assuming the model to hold the joint distribution of survival and censoring times is shown to be identifiable and the maximum likelihood estimator of the parameters is shown to be consistent

likelihood based inference for max stable processes the last decade has seen max stable processes emerge as a common tool for the statistical modeling of spatial extremes however their application is complicated due to the unavailability of the multivariate density function and so likelihood based methods remain far from providing a complete and flexible framework for inference in this article we develop inferentially practical likelihood based methods for fitting max stable processes derived from a composite likelihood approach the procedure is sufficiently reliable and versatile to permit the simultaneous modeling of marginal and dependence parameters in the spatial context at a moderate computational cost the utility of this methodology is examined via simulation and illustrated by the analysis of united states precipitation extremes

a note on pseudolikelihood constructed from marginal densities for likelihood based inference involving distributions in which high dimensional dependencies are present it may be useful to use approximate likelihoods based for example on the univariate or bivariate marginal distributions the asymptotic properties of formal maximum likelihood estimators in such cases are outlined in particular applications in which only a single q x i vector of observations is observed are examined conditions under which consistent estimators of parameters result from the approximate likelihood using only pairwise joint distributions are studied some examples are analysed in detail

the chirplet transform physical considerations we consider a multidimensional parameter space formed by inner products of a parameterizable family of chirp functions with a signal under analysis we propose the use of quadratic chirp functions which we will call q chirps for short giving rise to a parameter space that includes both the time frequency plane and the time scale plane as 2 d subspaces the parameter space contains a time frequency scale volume and thus encompasses both the short time fourier transform as a slice along the time and frequency axes and the wavelet transform as a slice along the time and scale axes in addition to time frequency and scale there are two other coordinate axes within this transform space shear in time obtained through convolution with a q chirp and shear in frequency obtained through multiplication by a q chirp signals in this multidimensional space can be obtained by a new transform which we call the q chirplet transform or simply the chirplet transform the proposed chirplets are generalizations of wavelets related to each other by 2 d affine coordinate transformations translations dilations rotations and shears in the time frequency plane as opposed to wavelets which are related to each other by 1 d affine coordinate transformations translations and dilations in the time domain only

asymptotic normality of extreme value estimators on c 0 1 consider n i i d random elements on c 0 1 we show that under an appropriate strengthening of the domain of attraction condition natural estimators of the extreme value index which is now a continuous function and the normalizing functions have a gaussian process as limiting distribution a key tool is the weak convergence of a weighted tail empirical process which makes it possible to obtain the results uniformly on 0 1 detailed examples are also presented

quotient correlation a sample based alternative to pearson s correlation the quotient correlation is defined here as an alternative to pearson s correlation that is more intuitive and flexible in cases where the tail behavior of data is important it measures nonlinear dependence where the regular correlation coefficient is generally not applicable one of its most useful features is a test statistic that has high power when testing nonlinear dependence in cases where the fisher s z transformation test may fail to reach a right conclusion unlike most asymptotic test statistics which are either normal or 2 this test statistic has a limiting gamma distribution henceforth the gamma test statistic more than the common usages of correlation the quotient correlation can easily and intuitively be adjusted to values at tails this adjustment generates two new concepts the tail quotient correlation and the tail independence test statistics which are also gamma statistics due to the fact that there is no analogue of the correlation coefficient in extreme value theory and there does not exist an efficient tail independence test statistic these two new concepts may open up a new field of study in addition an alternative to spearman s rank correlation a rank based quotient correlation is also defined the advantages of using these new concepts are illustrated with simulated data and a real data analysis of internet traffic

asymptotic behavior of bivariate gaussian powered extremes abstract in this paper joint asymptotics of powered maxima for a triangular array of bivariate gaussian random vectors are considered under the husler reiss condition limiting distributions of powered maxima are derived furthermore the second order expansions of the joint distributions of powered maxima are established under the refined husler reiss condition

geostatistics of extremes 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

the hybrid laplace transform finite element method applied to the quasi static and dynamic analysis of viscoelastic timoshenko beams the quasi static and dynamic responses of a linear viscoelastic beam are solved numerically by using the hybrid laplace transform finite element method in the analysis the timoshenko beam theory which includes the transverse shear and rotatory inertia effect and conventional beam theory are used to solve this problem the temperature field is assumed to be constant and homogeneous and that the relaxation modulus has the form of the prony series in the hybrid method the laplace transform with respect to time is applied to the coupled equations and the finite element model is developed by applying hamilton s variational principle without any integral transformation the numerical results of quasi static and dynamic responses for the models of maxwell fluid and three parameter solid types are presented and discussed

factor copula models for replicated spatial data abstractwe propose a new copula model that can be used with replicated spatial data unlike the multivariate normal copula the proposed copula is based on the assumption that a common factor exists and affects the joint dependence of all measurements of the process moreover the proposed copula can model tail dependence and tail asymmetry the model is parameterized in terms of a covariance function that may be chosen from the many models proposed in the literature such as the matern model for some choice of common factors the joint copula density is given in closed form and therefore likelihood estimation is very fast in the general case one dimensional numerical integration is needed to calculate the likelihood but estimation is still reasonably fast even with large datasets we use simulation studies to show the wide range of dependence structures that can be generated by the proposed model with different choices of common factors we apply the proposed model to spatial temperature data and com

a conditional approach for multivariate extreme values with discussion summary multivariate extreme value theory and methods concern the characterization estimation and extrapolation of the joint tail of the distribution of a d dimensional random variable existing approaches are based on limiting arguments in which all components of the variable become large at the same rate this limit approach is inappropriate when the extreme values of all the variables are unlikely to occur together or when interest is in regions of the support of the joint distribution where only a subset of components is extreme in practice this restricts existing methods to applications where d is typically 2 or 3 under an assumption about the asymptotic form of the joint distribution of a d dimensional random variable conditional on its having an extreme component we develop an entirely new semiparametric approach which overcomes these existing restrictions and can be applied to problems of any dimension we demonstrate the performance of our approach and its advantages over existing methods by using theoretical examples and simulation studies the approach is used to analyse air pollution data and reveals complex extremal dependence behaviour that is consistent with scientific understanding of the process we find that the dependence structure exhibits marked seasonality with ex tremal dependence between some pollutants being significantly greater than the dependence at non extreme levels

bivariate threshold methods for extremes summary an extension of the threshold method for extreme values is developed to consider the joint distribution of extremes of two variables the methodology is based on the point process representation of bivariate extremes both parametric and nonparametric models are considered the simplest case to handle is that in which both marginal distributions are known for the more realistic case in which the marginal distributions are unknown a mixed parametric nonparametric method is proposed the techniques are illustrated with data on sulphate and nitrate levels taken from a major study of acid rain

stationary max stable fields associated to negative definite functions let wi i be independent copies of a zero mean gaussian process w t t d with stationary increments and variance 2 t independently of wi let i 1 ui be a poisson point process on the real line with intensity e y dy we show that the law of the random family of functions vi i where vi t ui wi t 2 t 2 is translation invariant in particular the process t i 1 vi t is a stationary max stable process with standard gumbel margins the process arises as a limit of a suitably normalized and rescaled pointwise maximum of n i i d stationary gaussian processes as n if and only if w is a nonisotropic fractional brownian motion on d under suitable conditions on w the process has a mixed moving maxima representation

estimation of husler reiss distributions and brown resnick processes summary estimation of extreme value parameters from observations in the max domain of attraction of a multivariate max stable distribution commonly uses aggregated data such as block maxima multivariate peaks over threshold methods in contrast exploit additional information from the non aggregated large observations we introduce an approach based on peaks over thresholds that provides several new estimators for processes in the max domain of attraction of the frequently used husler reiss model and its spatial extension brown resnick processes the method relies on increments t0 conditional on t0 exceeding a high threshold where t0 is a fixed location when the marginals are standardized to the gumbel distribution these increments asymptotically form a gaussian process resulting in computationally simple estimates of the husler reiss parameter matrix and particularly enables parametric inference for brown resnick processes based on high dimensional multivariate densities this is a major advantage over composite likelihood methods that are commonly used in spatial extreme value statistics since they rely only on bivariate densities a simulation study compares the performance of the new estimators with other commonly used methods as an application we fit a non isotropic brown resnick process to the extremes of 12 year data of daily wind speed measurements

a dependence measure for multivariate and spatial extreme values properties and inference we present properties of a dependence measure that arises in the study of extreme values in multivariate and spatial problems for multivariate problems the dependence measure characterises dependence at the bivariate level for all pairs and all higher orders up to and including the dimension of the variable necessary and sufficient conditions are given for subsets of dependence measures to be self consistent that is to guarantee the existence of a distribution with such a subset of values for the dependence measure for pairwise dependence these conditions are given in terms of positive semidefinite matrices and non differentiable positive definite functions we construct new nonparametric estimators for the dependence measure which unlike all naive nonparametric estimators impose these self consistency properties as the new estimators provide an improvement on the naive methods both in terms of the inferential and interpretability properties their use in exploratory extreme value analyses should aid the identification of appropriate dependence models the methods are illustrated through an analysis of simulated multivariate data which shows that a lack of self consistency is frequently a problem with the existing estimators and by a spatial analysis of daily rainfall extremes in south west england which finds a smooth decay in extremal dependence with distance

efficient inference and simulation for elliptical pareto processes recent advances in extreme value theory have established ell pareto processes as the natural limits for extreme events defined in terms of exceedances of a risk functional here we provide methods for the practical modelling of data based on a tractable yet flexible dependence model we introduce the class of elliptical ell pareto processes which arise as the limit of threshold exceedances of certain elliptical processes characterized by a correlation function and a shape parameter an efficient inference method based on maximizing a full likelihood with partial censoring is developed novel procedures for exact conditional and unconditional simulation are proposed these ideas are illustrated using precipitation extremes in switzerland

characteristic functions of random variables attracted to 1 stable laws the domain of attraction of a 1 stable law on r d is characterized by the expansions of the characteristic functions of its elements

diagnostics for dependence within time series extremes summary the analysis of extreme values within a stationary time series entails various assumptions concerning its long and short range dependence we present a range of new diagnostic tools for assessing whether these assumptions are appropriate and for identifying structure within extreme events these tools are based on tail characteristics of joint survivor functions but can be implemented by using existing estimation methods for extremes of univariate independent and identically distributed variables our diagnostic aids are illustrated through theoretical examples simulation studies and by application to rainfall and exchange rate data on the basis of these diagnostics we can explain characteristics that are found in the observed extreme events of these series and also gain insight into the properties of events that are more extreme than those observed

efficient inference for spatial extreme value processes associated to log gaussian random functions 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 of models for the extreme values of spatial processes until recently inference for max stable processes has been restricted to the use of pairwise composite likelihoods due to intractability of higher dimensional distributions in this work we consider random fields that are in the domain of attraction of a widely used class of max stable processes namely those constructed via manipulation of log gaussian random functions for this class we exploit limiting d dimensional multivariate poisson process intensities of the underlying process for inference on all d vectors exceeding a high marginal threshold in at least one component employing a censoring scheme to incorporate information below the marginal threshold we also consider the d dimensional distributions for the equivalent max stable process and perform full likelihood inference by exploiting the methods of stephenson tawn 2005 where information on the occurrence times of extreme events is shown to dramatically simplify the likelihood the stephenson tawn likelihood is in fact simply a special case of the censored poisson process likelihood we assess the improvements in inference from both methods over pairwise likelihood methodology by simulation

assessing the performance of the independence method in modeling spatial extreme rainfall spatial statistical methods are often employed to improve precision when estimating marginal distributions of extreme rainfall methods such as max stable and copula models parameterize the spatial dependence and provide a continuous spatial representation alternatively the independence method can be used to estimate marginal parameters without the need for parameterizing the spatial dependence and this method has been under utilized in hydrologic applications this paper investigates the effectiveness of the independence method for marginal parameter estimation of spatially dependent extremes its performance is compared with three spatial dependence models max stable brown resnick max stable schlather and gaussian copula by means of a simulation study the independence method is statistically robust in estimating parameters and their associated confidence intervals for spatial extremes with various underlying dependence structures the spatial dependence models perform comparably with the independence method when the spatial dependence structure is correctly specified otherwise they exhibit considerably worse performance we conclude that the independence method is more appealing for modeling the marginal distributions of spatial extremes e g regional estimation of trends in rainfall extremes due to its greater robustness and simplicity the four statistical methods are illustrated using a spatial data set comprising 69 subdaily rainfall series from the greater sydney region australia

methods of interconversion between linear viscoelastic material functions part i a numerical method based on prony series abstract an efficient and accurate numerical method of interconversion between linear viscoelastic material functions based on a prony series representation is presented and tested using experimental data from selected polymeric materials the method is straightforward and applicable to interconversion between modulus and compliance functions in time frequency and laplace transform domains good agreement is shown between solutions obtained from the method in different domains a detailed computational procedure and selection of values for parameters involved in the method are presented and illustrated in particular the effects of different choices of relaxation and retardation times on the accuracy of the method are discussed the mathematical efficiency associated with prony series representations of both source and target transient material functions is fully utilized the method is general enough to cover both viscoelastic solids and liquids the tensile relaxation data from polymethyl methacrylate pmma and the shear storage compliance data from polyisobutylene are used in illustrating the method in a companion paper schapery and park 1998 an extended approximate analytical interconversion method is presented

modelling pairwise dependence of maxima in space we model pairwise dependence of temporal maxima such as annual maxima of precipitation that have been recorded in space either on a regular grid or at irregularly spaced locations the construction of our estimators stems from the variogram concept the asymptotic properties of our pairwise dependence estimators are established through properties of empirical processes the performance of our approach is illustrated by simulations and by the treatment of a real dataset in addition to bringing new results about the asymptotic behaviour of copula estimators the latter being linked to first order variograms one main advantage of our approach is to propose a simple connection between extreme value theory and geostatistics

analytical modeling of viscoelastic dampers for structural and vibration control different approaches to the mathematical modeling of viscoelastic dampers are addressed and their theoretical basis and performance are compared the standard mechanical model smm comprising linear springs and dashpots is shown to accurately describe the broad band rheological behavior of common viscoelastic dampers and be more efficient than other models such as the fractional derivative model and the modified power law the smm renders a prony series expression for the modulus and compliance functions in the time domain and the remarkable mathematical efficiency associated with the exponential basis functions of a prony series greatly facilitates model calibration and interconversion while cumbersome nonlinear regression is usually required for other models a simple collocation or least squares method can be used to fit the smm to available experimental data the model allows viscoelastic material functions to be readily determined either directly from the experimental data or through interconversion from a function established in another domain numerical examples on two common viscoelastic dampers demonstrate the advantages of the smm over fractional derivative and power law models detailed computational procedures for fitting and interconversion are discussed and illustrated published experimental data from a viscoelastic liquid damper and a viscoelastic solid damper are used in the examples

a moment estimator for the index of an extreme value distribution on generalise l estimateur bien connu de hill de l indice d une fonction de reparatition avec queue de variation reguliere a une estimation de l indice d une loi de valeurs extremes on demontre la convergence et la normalite asymptotique on utilise l estimateur pour certaines estimations comme celle d une quantile elevee et d un point d extremite

statistical inference for max stable processes in space and time max stable processes have proved to be useful for the statistical modelling of spatial extremes several families of max stable random fields have been proposed in the literature one such representation is based on a limit of normalized and rescaled pointwise maxima of stationary gaussian processes that was first introduced by kabluchko and co workers this paper deals with statistical inference for max stable space time processes that are defined in an analogous fashion we describe pairwise likelihood estimation where the pairwise density of the process is used to estimate the model parameters for regular grid observations we prove strong consistency and asymptotic normality of the parameter estimates as the joint number of spatial locations and time points tends to furthermore we discuss extensions to irregularly spaced locations a simulation study shows that the method proposed works well for these models

on the likelihood function of gaussian max stable processes summary wederiveaclosedformexpressionforthelikelihoodfunctionofagaussianmax stableprocessindexed by r d at p d 1 sites d 1 we demonstrate the gain in efficiency in the maximum composite likelihood estimators of the covariance matrix from p 2t op 3 sites in r 2 by means of a monte carlo