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Kernel Density Estimator From Ranked Set Samples

Author

Listed:
  • Johan Lim
  • Min Chen
  • Sangun Park
  • Xinlei Wang
  • Lynne Stokes

Abstract

We study kernel density estimator from the ranked set samples (RSS). In the kernel density estimator, the selection of the bandwidth gives strong influence on the resulting estimate. In this article, we consider several different choices of the bandwidth and compare their asymptotic mean integrated square errors (MISE). We also propose a plug-in estimator of the bandwidth to minimize the asymptotic MISE. We numerically compare the MISE of the proposed kernel estimator (having the plug-in bandwidth estimator) to its simple random sampling counterpart. We further propose two estimators for a symmetric distribution, and show that they outperform in MISE all other estimators not considering symmetry. We finally apply the methods in this article to analyzing the tree height data from Platt et al. (1988) and Chen et al. (2003).

Suggested Citation

  • Johan Lim & Min Chen & Sangun Park & Xinlei Wang & Lynne Stokes, 2014. "Kernel Density Estimator From Ranked Set Samples," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(10-12), pages 2156-2168, May.
    • Handle: RePEc:taf:lstaxx:v:43:y:2014:i:10-12:p:2156-2168
    DOI: 10.1080/03610926.2013.791372
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    Cited by:

    1. Hani Samawi & Haresh Rochani & JingJing Yin & Daniel Linder & Robert Vogel, 2018. "Notes on kernel density based mode estimation using more efficient sampling designs," Computational Statistics, Springer, vol. 33(2), pages 1071-1090, June.
    2. Eftekharian, A. & Razmkhah, M., 2017. "On estimating the distribution function and odds using ranked set sampling," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 1-10.

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