Some Asymptotic Results of Kernel Density Estimator in Length-Biased Sampling

Authors

  • M. Ajami Department of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran
  • S. Jomhoori Department of Statistics, Faculty of Sciences, University of Birjand, Birjand, Islamic Republic of Iran
  • V. Fakoor Department of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran
Abstract:

In this paper, we prove the strong uniform consistency and asymptotic normality of the kernel density estimator proposed by Jones [12] for length-biased data.The approach is based on the invariance principle for the empirical processes proved by Horváth [10]. All simulations are drawn for different cases to demonstrate both, consistency and asymptotic normality and the method is illustrated by real automobile brake pads data.

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Journal title

volume 24  issue 1

pages  55- 62

publication date 2013-03-01

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