Priority statement and some properties of t-lgHill estimator (original) (raw)
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Environmental data: multivariate Extreme Value Theory in practice
Let (X t ,Y t ) be a bivariate stationary time series in some environmental study. We are interested to estimate the failure probability defined as P(X t > x,Y t > y), where x and y are high return levels. For the estimation of high return levels, we consider three methods from univariate extreme value theory, two of which deal with the extreme clusters. We further derive estimators for the bivariate failure probability, based on Draisma et al. 's approach and on Heffernan and Tawn (2004)'s approach. The comparison on different estimators is demonstrated via a simulation study. To the best of our knowledge, this is the first time that such a comparative study is performed. Finally, we apply the procedures to the real data set and the results are discussed.
2019
• Extreme Value Theory has been asserting itself as one of the most important statistical theories for the applied sciences providing a solid theoretical basis for deriving statistical models describing extreme or even rare events. The efficiency of the inference and estimation procedures depends on the tail shape of the distribution underlying the data. In this work we will present a review of tests for assessing extreme value conditions and for the choice of the extreme value domain. Motivated by two real environmental problems we will apply those tests showing the need of performing such tests for choosing the most appropriate parameter estimation methods.
Extreme value theory in the analysis of environmental events
2018
WELCOME to the 12th Workshop on Statistics, Mathematics and Computation! We celebrate this meeting in Honour of Professor Carlos Braumann, for his brilliant career and outstanding contribution to the field of Statistics in Portugal and abroad, and to whom we are deeply grateful for all the support, kind and precious collaboration in our meetings! We are delighted to have this celebration fostering strong interaction between national and international researchers, leading to a successful commitment and enthusiasm on promoting research in and between the broad areas of Statistics, Mathematics and Computation. It is a great pleasure to receive all our guests and contributors from 9 to 10 th November in UBI-Universidade da Beira Interior, expressing our huge gratitude to the University Coordinators for kindly accepted to embrace this challenge of receiving us again! The WSMC was successfully organized in several places along these last 12 years and we believe that our meetings have been creating very nice opportunities for showcasing the growth and development of the focused main areas, at a time when so many new technologies are available and huge challenges are emerging. The idea exchanges between participants are always helpful for generating positive impact on propelling the advancement of science and technology and some of these results have been published in high standard Journals, special issues and Springer Series Books. Also in this 12th WSMC edition the participants will have several journal opportunities for papers submission. Selected papers, after review, will appear in Journal of Applied Statistics, Biometrical Letters, Biometrics & Biostatistics International Journal (BBIJ) and in a new Springer volume of the Series Contributions to Statistics. We are hightly grateful to all the participants, Invited Speakers, Session Organizers and Authors who submitted abstracts, for their valuable contribution and for the enthusiastic way how they assume their participation. We also acknowledge all the sponsors and contributors who made this meeting a reality. Furthermore, we acknowledge the Rector of Universidade da Beira Interior, the Rector of Universidade Aberta, the Coordinator of the Centro de Estatística e Aplicações da Universidade de Lisboa and the President of the Committee on Risk Analysis of International Statistical Institute, for v vi Preface their support. We are most grateful to all the members of the Organizing Committee and of the Scientific Committee for their crucial help and suggestions. We address a deeply thanks to the Local Chair, Sandra Ferreira, and also to Amílcar Oliveira, Célia Nunes, Dário Ferreira and Luís Grilo for their invaluable contribution on organizing the Webpage, the final programme, the Book of Abstracts and so many details in a such incredible short time! Finally, the venue adds an important attraction to the meeting. The destination city, Covilhã, is a fantastic place close to beautiful and highest mountain in Portugal, Serra da Estrela.
Extreme value statistics: potential benefits in water quality management
Water Science and Technology, 1997
Recently extreme value statistics have been proved useful in environmental applications like the assessment of sea-levels, wind speeds and ozone concentrations. In this paper, after a brief overview of the statistical theory of extreme values, modelling issues are discussed with stress on applications in water quality management. Risk analysis procedures are presented that consider the extremal behaviour of water quality in the design stage of environmental constructions.
On the comparison of several classical estimators of the extreme value index
Communications in Statistics - Theory and Methods, 2020
Due to the fact that for heavy tails the classical Hill estimator of a positive extreme value index is asymptotically biased, new and interesting alternative estimators have appeared in the literature. In this work we compare several classical estimators of the extreme value index based on moments of the upper order statistics. Since several alternative estimators have eventually a null asymptotic bias, for some heavy tailed models, the comparison is performed not only with the Hill and recent generalized means estimators but also with an asymptotically unbiased Hill estimator. The comparison study is performed asymptotically, under a third-order framework, and for finite samples, through a Monte Carlo simulation study.
On ecological aspects of dynamics for zero slope regression for water pollution in Chile
Stochastic Analysis and Applications, 2019
Zero slope regression is an important problem in chemometrics, ranging from challenges of intercept-bias and slope 'corrections' in spectrometry, up to analysis of administrative data on chemical pollution in water in the region of Arica and Parinacota. Such issue is really complex and it integrates problems of optimal design, symmetry of errors, stabilization of the variability of estimators, dynamical system for errors up to an administrative data challenges. In this article we introduce a realistic approach to zero slope regression problem from dynamical point of view. Linear regression is a widely used approach for data fitting under assumption of normally distributed residuals. Many times non-normal residuals are observed and also theoretically justified. Our solution to such problem uses the recently introduced inference function called score function of distribution. As a minimization criterion, the minimum information of residuals criterion is used. The score regression appears to be a direct generalization of the least-squares regression for an arbitrary known (believed) distribution of residuals. The score estimation is also distribution sensitive version of M-estimation. The capability of the method is demonstrated by water pollution data examples.
Analyses of Environmental time series: Extreme Values
2015
The knowledge of extreme events of environmental variables is an issue of increasing concern to the scientific community. Within the branch of coastal and ocean engineering there are many fields of application where an accurate estimation of long term return period events is needed, i.e. coastal defenses design, coastal flooding management, estimation of changes of the littoral morphology, offshore and onshore renewable energy devices design, etc. But not only the engineers are concerned by extreme events; biological communities in the open sea and estuarine systems are also exposed to extreme events that may affect its natural development (i.e. extreme sea levels in estuarine environments could raze fields of plants not able to deal with salt in just a few hours). But the analysis of environmental variables and their extreme behaviors is not an easy task. In most cases the problem to be solved presents a multivariate nature, which makes it of a special complexity. For instance, in ...
Revisiting the maximum likelihood estimation of a positive extreme value index
Journal of Statistical Theory and Practice, 2014
In this paper we revisit Feuerverger and Hall's maximum likelihood estimation of the extreme value index. Based on those estimators we propose new estimators that have the smallest possible asymptotic variance, equal to the asymptotic variance of the Hill estimator. The full asymptotic distributional properties of the estimators are derived under a general third-order framework for heavy tails. Applications to a real data set and to simulated data are also presented.
Improved estimation procedures for a positive extreme value index
2010
By submitting this dissertation electronically, I declare that the entirety of the work contained therein is my own, original work, that I am the authorship owner thereof (unless to the extent explicitly otherwise stated) and I have not previously in its entirety or in part submitted it for obtaining any qualification.
Bayesian non-asymptotic extreme value models for environmental data
2020
Motivated by the analysis of extreme rainfall data, we introduce a general Bayesian hierarchical model for estimating the probability distribution of extreme values of intermittent random sequences, a common problem in geophysical and environmental science settings. The approach presented here relaxes the asymptotic assumption typical of the traditional extreme value (EV) theory, and accounts for the possible underlying variability in the distribution of event magnitudes and occurrences, which are described through a latent temporal process. Focusing on daily rainfall extremes, the structure of the proposed model lends itself to incorporating prior geo-physical understanding of the rainfall process. By means of an extensive simulation study, we show that this methodology can significantly reduce estimation uncertainty with respect to Bayesian formulations of traditional asymptotic EV methods, particularly in the case of relatively small samples. The benefits of the approach are furt...