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A Berry‐Esseen Type Bound in Kernel Density Estimation for Negatively Associated Censored Data

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  • Qunying Wu
  • Pingyan Chen

Abstract

We discuss the kernel estimation of a density function based on censored data when the survival and the censoring times form the stationary negatively associated (NA) sequences. Under certain regularity conditions, the Berry‐Esseen type bounds are derived for the kernel density estimator and the Kaplan‐Meier kernel density estimator at a fixed point x.

Suggested Citation

  • Qunying Wu & Pingyan Chen, 2013. "A Berry‐Esseen Type Bound in Kernel Density Estimation for Negatively Associated Censored Data," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:541250
    DOI: 10.1155/2013/541250
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    References listed on IDEAS

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    1. R.D. Gill, 1980. "Censoring and Stochastic Integrals," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 34(2), pages 124-124, June.
    2. Zhang, Li-Xin, 2001. "The Weak Convergence for Functions of Negatively Associated Random Variables," Journal of Multivariate Analysis, Elsevier, vol. 78(2), pages 272-298, August.
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