caa a22 4500 605463794 CHVBK 20210128100255.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s10687-015-0219-z doi (NATIONALLICENCE)springer-10.1007/s10687-015-0219-z Nonparametric adaptive estimation of conditional probabilities of rare events and extreme quantiles [Elektronische Daten] [Gilles Durrieu, Ion Grama, Quang-Khoai Pham, Jean-Marie Tricot] Let F t (x)=P(X≤x|T=t) be the conditional distribution of a random variable X given that a covariate T takes the value t ∈ [ 0 , T max ] , $t \in [0,T_{\max }],$ where we assume that the distributions F t are in the domain of attraction of the Fréchet distribution. We observe independent random variables X t 1 , ... , X t n $X_{t_{1}},...,X_{t_{n}}$ associated to a sequence of times 0 ≤ t 1 < ... < t n ≤ T max , $0\leq t_{1}<...<t_{n}\leq T_{\max },$ where X t i $X_{t_{i}}$ has the distribution function F t i . $F_{t_{i}}.$ For each t ∈ [ 0 , T max ] $t\in [0,T_{\max }]$ , we propose a nonparametric adaptive estimator for extreme tail probabilities and quantiles of F t . It follows from the Fisher-Tippett-Gnedenko theorem that the tail of the distribution function F t can be adjusted with a Pareto distribution of parameter 𝜃 t,τ starting from a threshold τ. We estimate the parameter 𝜃 t,τ using a nonparametric kernel estimator of bandwidth h based on the observations larger than τ and we propose a pointwise data driven procedure to choose the threshold τ. A global selection of the bandwidth h based on a cross-validation approach is given. Under some regularity assumptions, we prove that the non adaptive and adaptive estimators of 𝜃 t,τ are consistent and we determine their rate of convergence. Finally, we study this procedure using simulations and we analyze an environmental data set. Springer Science+Business Media New York, 2015 Nonparametric estimation nationallicence Tail conditional probabilities nationallicence Extreme conditional quantile nationallicence Adaptive estimation nationallicence Environment nationallicence Durrieu Gilles Université de Bretagne Sud, LMBA, UMR CNRS 6205, 56000, Vannes, France aut Grama Ion Université de Bretagne Sud, LMBA, UMR CNRS 6205, 56000, Vannes, France aut Pham Quang-Khoai Université de Bretagne Sud, LMBA, UMR CNRS 6205, 56000, Vannes, France aut Tricot Jean-Marie Université de Bretagne Sud, LMBA, UMR CNRS 6205, 56000, Vannes, France aut Extremes Springer US; http://www.springer-ny.com 18/3(2015-09-01), 437-478 1386-1999 18:3<437 2015 18 10687 https://doi.org/10.1007/s10687-015-0219-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10687-015-0219-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Durrieu Gilles Université de Bretagne Sud, LMBA, UMR CNRS 6205, 56000, Vannes, France aut NATIONALLICENCE 700 1- Grama Ion Université de Bretagne Sud, LMBA, UMR CNRS 6205, 56000, Vannes, France aut NATIONALLICENCE 700 1- Pham Quang-Khoai Université de Bretagne Sud, LMBA, UMR CNRS 6205, 56000, Vannes, France aut NATIONALLICENCE 700 1- Tricot Jean-Marie Université de Bretagne Sud, LMBA, UMR CNRS 6205, 56000, Vannes, France aut NATIONALLICENCE 773 0- Extremes Springer US; http://www.springer-ny.com 18/3(2015-09-01), 437-478 1386-1999 18:3<437 2015 18 10687