[Normalité asymptotique de la méthode ET – application au test ET]
Nous proposons un test permettant de vérifier l'adéquation de la queue d'une fonction de répartition F0 aux observations extrêmes et de contrôler si cette queue fournit des extrapolations raisonnables au-delà de l'observation maximale. Le test est basé sur la loi asymptotique de l'estimateur ET (Exponential Tail) des quantiles extrêmes qui est établie dans une Note jointe. Le niveau et la puissance asymptotiques du test sont étudiés pour plusieurs classes de lois.
We propose a procedure to test the adequacy of the tail of a given F0 to extreme observations and to check that this tail provides reasonable extrapolations above the maximal observation. The test is based on the asymptotic distribution of the ET (Exponential Tail) estimate of extreme quantiles which is established in a companion Note. The asymptotic level and power of the test are studied for several classes of distributions.
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@article{CRMATH_2003__337_3_213_0,
author = {Diebolt, Jean and Garrido, Myriam and Girard, St\'ephane},
title = {Asymptotic normality of the {ET} method {\textendash} application to the {ET~test}},
journal = {Comptes Rendus. Math\'ematique},
pages = {213--218},
publisher = {Elsevier},
volume = {337},
number = {3},
year = {2003},
doi = {10.1016/S1631-073X(03)00238-3},
language = {en},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(03)00238-3/}
}
TY - JOUR AU - Diebolt, Jean AU - Garrido, Myriam AU - Girard, Stéphane TI - Asymptotic normality of the ET method – application to the ET test JO - Comptes Rendus. Mathématique PY - 2003 SP - 213 EP - 218 VL - 337 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(03)00238-3/ DO - 10.1016/S1631-073X(03)00238-3 LA - en ID - CRMATH_2003__337_3_213_0 ER -
%0 Journal Article %A Diebolt, Jean %A Garrido, Myriam %A Girard, Stéphane %T Asymptotic normality of the ET method – application to the ET test %J Comptes Rendus. Mathématique %D 2003 %P 213-218 %V 337 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(03)00238-3/ %R 10.1016/S1631-073X(03)00238-3 %G en %F CRMATH_2003__337_3_213_0
Diebolt, Jean; Garrido, Myriam; Girard, Stéphane. Asymptotic normality of the ET method – application to the ET test. Comptes Rendus. Mathématique, Tome 337 (2003) no. 3, pp. 213-218. doi : 10.1016/S1631-073X(03)00238-3. http://www.numdam.org/articles/10.1016/S1631-073X(03)00238-3/
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