Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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A Berry-Esseen Type Bound in Kernel Density Estimation for a Random Left-Truncation Model

  • Asghari, P. (Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad) ;
  • Fakoor, V. (Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad) ;
  • Sarmad, M. (Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad)
  • Received : 2013.07.29
  • Accepted : 2014.01.22
  • Published : 2014.03.31
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Abstract

In this paper we derive a Berry-Esseen type bound for the kernel density estimator of a random left truncated model, in which each datum (Y) is randomly left truncated and is sampled if $Y{\geq}T$, where T is the truncation random variable with an unknown distribution. This unknown distribution is estimated with the Lynden-Bell estimator. In particular the normal approximation rate, by choice of the bandwidth, is shown to be close to $n^{-1/6}$ modulo logarithmic term. We have also investigated this normal approximation rate via a simulation study.

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References

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