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Conventional geostatistical methodology solves the problem of predicting the re-alised value of a linear functional of a Gaussian spatial stochastic process, S(x), based on observations Y i = S(x i) + Z i at sampling locations x i , where the Z i are mutually independent, zero-mean Gaussian random variables. We describe two spatial applications for which(More)
SUMMARY 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(More)
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(More)
for helpful comments. We are grateful to the referee and the editor for their comments and suggestions that result in a substantial improvement of this manuscript. Abstract This paper presents a general framework for identifying and modelling joint-tail distribution based on multivariate extreme value theories. We argue that the multivariate approach is the(More)
In this paper we propose a new particle smoother that has a computational complexity of O(N), where N is the number of particles. This compares favourably with the O(N 2) computational cost of most smoothers and will result in faster rates of convergence for fixed computational cost. The new method also overcomes some of the degeneracy problems we identify(More)
Smith and Weissman introduced a M4 class of processes which are very flexible models for temporally dependent multivariate extreme value processes. However all variables in these M4 models are asymptotically dependent and what this paper does is to extend this M4 class in a number of ways to produce classes of models which are also asymptotically(More)
SUMMARY The modelling of extremes of a time series has progressed from the assumption of independent observations to more realistic forms of temporal dependence. In this paper, we focus on Markov chains, deriving a class of models for their joint tail which allows the degree of clustering of extremes to decrease at high levels, overcoming a key limitation(More)