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On the weak convergence and Central Limit Theorem of blurring and nonblurring processes with application to robust location estimation

Author

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  • Chen, Ting-Li
  • Fujisawa, Hironori
  • Huang, Su-Yun
  • Hwang, Chii-Ruey

Abstract

This article studies the weak convergence and associated Central Limit Theorem for blurring and nonblurring processes. Then, they are applied to the estimation of location parameter. Simulation studies show that the location estimation based on the convergence point of blurring process is more robust and often more efficient than that of nonblurring process.

Suggested Citation

  • Chen, Ting-Li & Fujisawa, Hironori & Huang, Su-Yun & Hwang, Chii-Ruey, 2016. "On the weak convergence and Central Limit Theorem of blurring and nonblurring processes with application to robust location estimation," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 165-184.
    • Handle: RePEc:eee:jmvana:v:143:y:2016:i:c:p:165-184
    DOI: 10.1016/j.jmva.2015.09.009
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    References listed on IDEAS

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    1. Ting-Li Chen, 2015. "On the convergence and consistency of the blurring mean-shift process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 157-176, February.
    2. Fujisawa, Hironori & Eguchi, Shinto, 2008. "Robust parameter estimation with a small bias against heavy contamination," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2053-2081, October.
    3. Aliyari Ghassabeh, Youness, 2015. "A sufficient condition for the convergence of the mean shift algorithm with Gaussian kernel," Journal of Multivariate Analysis, Elsevier, vol. 135(C), pages 1-10.
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