Time varying extremes for monitoring aquatic biosensors

Gilles Durrieu (1) , Ion Grama (1) , Quang-Khoai Pham (1) , Jean-Marie Tricot (1)

1 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

Measurement of mollusks bivalves activity is a way to record the animal behavior and so to evaluate possible changes in the water quality. In the framework of ecological time series data at times 0 < t1 < ::: < tn T; we observe independent observations Xt1 ; :::;Xtn where each Xti is distributed according to the distribution function Fti : For each t 2 [0; T], we propose a non parametric adaptive estimator for tail probabilities and extreme quantiles of Ft: The idea of our approach is to adjust the tail of the distribution function Ft with a Pareto distribution with parameter t; starting from a threshold . The parameter t; is estimated using a non parametric kernel estimator of bandwidth h based on the observations larger than : Under some regularity assumptions, we prove that the proposed adaptive estimator of t; is consistent and we determine its rate of convergence. We also propose a sequential testing based procedure for the automatic choice of the threshold when the bandwidth h is xed. Finally, we study the properties of this procedure by simulation and on real data set to estimate global changes (pollution, temperature change) and so to help in the survey of aquatic systems.

Mots clés: Applications and Case Studies; Quantile Estimation; Nonparametric Methods; Extreme Value Theory; Time Series

Domaines: Applications [stat.AP]

Gilles Durrieu, Ion Grama, Quang-Khoai Pham, Jean-Marie Tricot. Time varying extremes for monitoring aquatic biosensors. 2013. ⟨hal-00918833⟩