Nonparametric adaptive estimation of conditional probabilities of rare events and extreme quantiles

Durrieu, Gilles; Grama, Ion; Pham, Quang-Khoai; Tricot, Jean-Marie

doi:10.1007/s10687-015-0219-z

Cited by 23 publications

(33 citation statements)

References 45 publications

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“…We focus on a statistical procedure developed in Durrieu et al (2015) to determine the extremal valve closing velocities (X t ) t∈[0,T max ] of oysters as a function of time based on the extreme values modeling.…”

Section: Statistical Modelingmentioning

confidence: 99%

“…Following Grama and Spokoiny (2008), Durrieu et al (2015) and Eq. 1, the distribution function F t can be approximated as the threshold τ converges to infinity by the following semi-parametric model:…”

Section: Statistical Modelingmentioning

confidence: 99%

“…The estimators θ t,h,τ , F t,h,τ (x) and q p (t, h, τ ) depend on the unknown parameters τ and h. In Grama and Spokoiny (2008) and Durrieu et al (2015), it is proposed to choose the threshold parameter τ by an adaptive procedure based on sequential multiple testing procedure. A selection procedure for the bandwidth h is also given using a modified cross validation method.…”

Section: Statistical Modelingmentioning

confidence: 99%

“…A selection procedure for the bandwidth h is also given using a modified cross validation method. The asymptotic properties (consistence and rates of convergence) of the estimators of θ t , the extreme quantile of order p, and the tail probability are studied in Durrieu et al (2015). The properties of our approach have been studied through simulations that demonstrated the accuracy of the procedure for estimating the model parameters and its performance for independent and dependent data.…”

Section: Statistical Modelingmentioning

confidence: 99%

See 3 more Smart Citations

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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Section: Statistical Modelingmentioning

confidence: 99%

Section: Statistical Modelingmentioning

confidence: 99%

Section: Statistical Modelingmentioning

confidence: 99%

Section: Statistical Modelingmentioning

confidence: 99%

See 2 more Smart Citations

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

Self Cite

View full text Add to dashboard Cite

show abstract

“…We refer to Hall and Welsh (1985), Drees and Kaufmann (1998), Guillou and Hall (2001), Huisman, Koedijk, Kool, and Palm (2001), Beirlant, Goegebeur, Teugels, and Segers (2004), Spokoiny (2008, 2007) and El Methni, Gardes, Girard, and Guillou (2012) where several procedures for choosing the threshold τ have been proposed. Here, we adopt the method from Grama and Spokoiny (2008) and Durrieu, Grama, Pham, and Tricot (2015). The package extremefit includes the modeling of time dependent data.…”

Section: Introductionmentioning

confidence: 99%