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Some Functional Large Deviations Principles in Nonparametric Function Estimation

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Date
2012
Dewey
Probabilités et mathématiques appliquées
Sujet
Weak topology; Delta-sequence; Density; Estimation; Large deviation; Regression
Journal issue
Journal of Theoretical Probability
Volume
25
Number
1
Publication date
2012
Article pages
280-309
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s10959-011-0342-y
URI
https://basepub.dauphine.fr/handle/123456789/6049
Collections
  • CEREMADE : Publications
Metadata
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Author
Louani, Djamal
Ould Maouloud, Sidi Mohamed
Type
Article accepté pour publication ou publié
Abstract (EN)
In this paper, we investigate functional large deviation behaviors of some nonparametric function estimates. As a first step, we define a a vector process W n and study its large deviation behavior in the space L 1×L 1×L 1 with respect to the weak convergence topology. As by-products, we derive large deviation principles in the L 1-space equipped with the weak convergence topology simultaneously for several density and regression estimators built up using the delta-sequence estimation method.

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