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Article Dans Une Revue Journal of Nonparametric Statistics Année : 2006

Sharp large deviations in nonparametric estimation

Résumé

Large deviation results for the kernel density estimator and the kernel regression estimator have been given by Louani [Louani, D., 1998, Large deviations limit theorems for the kernel density estimator. Scandinavian Journal of Statistics, 25, 243–253; Louani, D., 1999, Some large deviations limit theorems in conditional nonparametric statistics. Statistics, 33, 171–196]. We complete these works by establishing sharp large deviation results for the two estimators. This means that we study precisely the tail probabilities of the estimators. We distinguish two cases depending on the support of the kernel. To prove the results, we need an Edgeworth expansion obtained from a version of Cramer’s condition.

Dates et versions

hal-01817770 , version 1 (18-06-2018)

Identifiants

Citer

Cyrille Joutard. Sharp large deviations in nonparametric estimation. Journal of Nonparametric Statistics, 2006, 18 (3), pp.293 - 306. ⟨10.1080/10485250600819233⟩. ⟨hal-01817770⟩
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