Multivariate nonparametric estimation of the Pickands dependence function using Bernstein polynomials

Autor: Giulia Marcon, Simone A. Padoan, Johan Segers, Philippe Naveau, Pietro Muliere
Přispěvatelé: Laboratoire des Sciences du Climat et de l'Environnement [Gif-sur-Yvette] (LSCE), Institut national des sciences de l'Univers (INSU - CNRS)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), Extrèmes : Statistiques, Impacts et Régionalisation (ESTIMR), Institut national des sciences de l'Univers (INSU - CNRS)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Marcon G., Padoan S.A., Naveau P., Muliere P., Segers J.
Jazyk: angličtina
Rok vydání: 2017
Předmět:
Statistics and Probability
FOS: Computer and information sciences
Multivariate statistics
NONPARAMETRIC ESTIMATION
MULTIVARIATE MAX-STABLE DISTRIBUTION
01 natural sciences
Copula (probability theory)
Methodology (stat.ME)
010104 statistics & probability
Statistics
Statistics::Methodology
0101 mathematics
Extreme-value copula
EXTREMAL DEPENDENCE
EXTREMEVALUE COPULA
[SDU.ENVI]Sciences of the Universe [physics]/Continental interfaces
environment
Statistics - Methodology
ComputingMilieux_MISCELLANEOUS
Mathematics
[SDU.OCEAN]Sciences of the Universe [physics]/Ocean
Atmosphere
Applied Mathematics
010102 general mathematics
Nonparametric statistics
Estimator
Extremal dependence
HEAVY RAINFALL
Bernstein polynomial
BERNSTEIN POLYNOMIALS
EXTREMAL DEPENDENCE
EXTREMEVALUE COPULA
HEAVY RAINFALL
NONPARAMETRIC ESTIMATION
MULTIVARIATE MAX-STABLE DISTRIBUTION
PICKANDS DEPENDENCE FUNCTION
13. Climate action
Dependence function
Statistics
Probability and Uncertainty
Maxima
Settore SECS-S/01 - Statistica
BERNSTEIN POLYNOMIALS
PICKANDS DEPENDENCE FUNCTION
Zdroj: Journal of Statistical Planning and Inference
Journal of Statistical Planning and Inference, Elsevier, 2017, 183, pp.1-17. ⟨10.1016/j.jspi.2016.10.004⟩
Journal of Statistical Planning and Inference, 2017, 183, pp.1-17. ⟨10.1016/j.jspi.2016.10.004⟩
ISSN: 0378-3758
1873-1171
DOI: 10.1016/j.jspi.2016.10.004⟩
Popis: Many applications in risk analysis require the estimation of the dependence among multivariate maxima, especially in environmental sciences. Such dependence can be described by the Pickands dependence function of the underlying extreme-value copula. Here, a nonparametric estimator is constructed as the sample equivalent of a multivariate extension of the madogram. Shape constraints on the family of Pickands dependence functions are taken into account by means of a representation in terms of Bernstein polynomials. The large-sample theory of the estimator is developed and its finite-sample performance is evaluated with a simulation study. The approach is illustrated with a dataset of weekly maxima of hourly rainfall in France recorded from 1993 to 2011 at various weather stations all over the country. The stations are grouped into clusters of seven stations, where our interest is in the extremal dependence within each cluster.
Databáze: OpenAIRE
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