Some Functional Large Deviations Principles in Nonparametric Function Estimation

Djamal Louani () and Sidi Mohamed Ould Maouloud
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Djamal Louani: Université de Paris 6
Sidi Mohamed Ould Maouloud: Université de Paris-Dauphine

Journal of Theoretical Probability, 2012, vol. 25, issue 1, 280-309

Abstract: Abstract 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.

Keywords: Delta-sequence; Density; Estimation; Large deviation; Regression; Weak topology; 60F10; 62G07; 62G08 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10959-011-0342-y

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