Tail Index Estimation, Pareto Quantile Plots, and Regression Diagnostics

Beirlant, Jan; Vynckier, Petra; Teugels, Jozef L.

doi:10.2307/2291593

Cited by 109 publications

(89 citation statements)

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“…Beirlant et al (2004), Reiss and Thomas (2007), and references therein). Approaches to this estimation may be classified into two classes, supervised procedures in which the threshold to estimate the tail is chosen according to the problem (as e.g., for seminal references, the weighted moments- (Hosking and Wallis 1987), the MEP-(Davison and Smith 1990), Hill-(Hill 1975), QQ- (Kratz and Resnick 1996), (Beirlant et al 1996) methods), and unsupervised ones, where the threshold is algorithmically determined (as e.g. in Bengio and Carreau (2009) and references therein, Debbabi and Kratz (2014)).…”

Section: Resultsmentioning

confidence: 99%

Normex, a new method for evaluating the distribution of aggregated heavy tailed risks

Kratz

2014

Extremes

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We develop theoretically as well as numerically a new method, Normex, for the sum of independent heavy tailed distributed random variables, to obtain the most accurate evaluation of its entire distribution. Normex provides sharp results, whatever the number of summands and the tail index are. It is particularly suited when the Central Limit Theorem (CLT) applies but with slow convergence of the mean and with a poor approximation for the tail. Hence, it is filling up a gap in the literature by giving an appropriate limit distribution in this case, in general better than with most standard methods. An application is developed to evaluate the Value-atRisk of the yearly log returns of financial assets. AMS 2000 Subject ClassificationsMarie Kratz is also member of MAP5, UMR 8145, Univ. Paris Descartes,

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Section: Resultsmentioning

confidence: 99%

Normex, a new method for evaluating the distribution of aggregated heavy tailed risks

Kratz

2014

Extremes

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“…We also estimate the extreme p-quantile for each t in the interval [0, T max ], where p is a quantile order chosen to be close to 1. The distributions F t are in the domain of attraction of the Fréchet distribution according to the Pareto quantile plot method as described in Beirlant et al (1996). The graphical plot results are not given.…”

Section: Statistical Modelingmentioning

confidence: 99%

Dynamic extreme values modeling and monitoring by means of sea shores water quality biomarkers and valvometry

Durrieu

Pham

Foltête

et al. 2016

Environ Monit Assess

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Water quality can be evaluated using biomarkers such as tissular enzymatic activities of endemic species. Measurement of molluscs bivalves activity at high frequency (e.g., valvometry) during a long time period is another way to record the animal behavior and to evaluate perturbations of the water quality in real time. As the pollution affects the activity of oysters, we consider the valves opening and closing velocities to monitor the water quality assessment. We propose to model the huge volume of velocity data collected in the framework of valvometry using a new nonparametric extreme values statistical model. The objective is to estimate the tail probabilities and the extreme quantiles of the distribution of valve closing velocity. The tail of the distribution function of valve closing velocity is modeled by a Pareto distribution with parameter 𝜃 t,τ , beyond a threshold τ according to the time t of the experiment. Our modeling approach reveals the dependence between the specific activity of two enzymatic biomarkers (Glutathione-S-transferase and acetylcholinesterase) and the continuous recording of oyster valve velocity, proving the suitability of this tool for water quality assessment. Thus, valvometry allows in real-time in situ analysis of the bivalves behavior and appears as an effective early warning tool in ecological risk assessment and marine environment monitoring.

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“…Regardless of some efforts to find an appropriate mechanism 17 there is not a reliable method to calculate it, hence the current study favours a technique based on the analysis of an array of elements such as the sample Mean Excess Function (MEF), QQ plots, sample Kernel Density and sample Quantile Function, following Reiss and Thomas (2007) and McNeil and Saladin (1997). The threshold u would denote the value from where the MEF exhibits a positive gradient (excesses follow a GPD with > 0), provided the estimated 17 Reiss and Thomas (2007) or Beirlant et al (1996) explain methods which seem to work reasonably well but should be handled with care, as they may eventually result in the selection of a very high number of upper order statistics. Danielsson et al (1998) and Coronel-Brinzio and Hernandez-Montoya (2004) introduce interesting approaches to this subject.…”

Section: Extreme Value Theory (Evt)mentioning

confidence: 99%