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Some Functional Large Deviations Principles in Nonparametric Function Estimation

Louani, Djamal; Ould Maouloud, Sidi Mohamed (2012), Some Functional Large Deviations Principles in Nonparametric Function Estimation, Journal of Theoretical Probability, 25, 1, p. 280-309. http://dx.doi.org/10.1007/s10959-011-0342-y

Type
Article accepté pour publication ou publié
Date
2012
Journal name
Journal of Theoretical Probability
Volume
25
Number
1
Publisher
Springer
Pages
280-309
Publication identifier
Metadata
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Author(s)
Louani, Djamal
Ould Maouloud, Sidi Mohamed
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.
Subjects / Keywords
Weak topology; Delta-sequence; Density; Estimation; Large deviation; Regression