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Some Functional Large Deviations Principles in Nonparametric Function Estimation

Author

Listed:
  • Djamal Louani

    (Université de Paris 6)

  • Sidi Mohamed Ould Maouloud

    (Université de Paris-Dauphine)

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.

Suggested Citation

  • Djamal Louani & Sidi Mohamed Ould Maouloud, 2012. "Some Functional Large Deviations Principles in Nonparametric Function Estimation," Journal of Theoretical Probability, Springer, vol. 25(1), pages 280-309, March.
    • Handle: RePEc:spr:jotpro:v:25:y:2012:i:1:d:10.1007_s10959-011-0342-y
    DOI: 10.1007/s10959-011-0342-y
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    References listed on IDEAS

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    1. Djamal Louani, 1998. "Large Deviations Limit Theorems for the Kernel Density Estimator," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 243-253, March.
    2. Fuqing Gao, 2003. "Moderate Deviations and Large Deviations for Kernel Density Estimators," Journal of Theoretical Probability, Springer, vol. 16(2), pages 401-418, April.
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