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Asymptotic Properties of a Nonparametric Regression Function Estimator with Randomly Truncated Data

  • Elias Ould-Saïd
  • Mohamed Lemdani
Article

Abstract

In this paper, we define a new kernel estimator of the regression function under a left truncation model. We establish the pointwise and uniform strong consistency over a compact set and give a rate of convergence of the estimate. The pointwise asymptotic normality of the estimate is also given. Some simulations are given to show the asymptotic behavior of the estimate in different cases. The distribution function and the covariable’s density are also estimated.

Keywords

Asymptotic normality Kernel Nonparametric regression Rate of convergence Strong consistency Truncated data V-C class 

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Copyright information

© The Institute of Statistical Mathematics, Tokyo 2006

Authors and Affiliations

  1. 1.L.M.P.A. J. LiouvilleUniv. du Littoral Côte d’OpaleCalaisFrance
  2. 2.Lab. Biomaths-EA 3614Univ. de Lille 2LilleFrance

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