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Large deviations for bootstrapped empirical measures

Wintenberger, Olivier; Trashorras, José (2014), Large deviations for bootstrapped empirical measures, Bernoulli, 20, 4, p. 1845-1878. http://dx.doi.org/10.3150/13-BEJ544

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Article accepté pour publication ou publié
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http://hal.archives-ouvertes.fr/hal-00633707/fr/
Date
2014
Nom de la revue
Bernoulli
Volume
20
Numéro
4
Éditeur
Bernoulli Society for Mathematical Statistics and Probability
Pages
1845-1878
Identifiant publication
Métadonnées
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Auteur(s)
Wintenberger, Olivier
Trashorras, José
Résumé (EN)
We investigate the Large Deviations (LD) properties of bootstrapped empirical measures with exchangeable weights. Our main results show in great generality how the resulting rate functions combine the LD properties of both the sample weights and the observations. As an application, we obtain new LD results and discuss both conditional and unconditional LD-efficiency for many classical choices of entries such as Efron’s, leave-p-out, i.i.d. weighted, k-blocks bootstraps, etc.
Mots-clés
Exchangeable bootstrap; Large deviations