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Simulated annealing for higher dimensional projection depth

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  • Shao, Wei
  • Zuo, Yijun

Abstract

Data depth for multivariate data has received considerable attention in multivariate nonparametric analysis and robust statistics. Nevertheless, the computation of data depth such as projection depth has remained as a very challenging problem which hinders the development of the projection depth and its wide use in practice. Especially in high dimension, there is no efficient algorithm for the computation of the projection depth and its induced estimators (including the Stahel–Donoho estimator as a special case). In this paper, we employ simulated annealing algorithm by invoking Markov Chain Monte Carlo technique to compute the projection depth. Simulation results show that this new approximate method performs significantly better than its competitors. In lower dimension, we are able to show that the approximate results from this algorithm are very close to the exact ones.

Suggested Citation

  • Shao, Wei & Zuo, Yijun, 2012. "Simulated annealing for higher dimensional projection depth," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4026-4036.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:12:p:4026-4036
    DOI: 10.1016/j.csda.2012.05.002
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    References listed on IDEAS

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    1. Zuo, Yijun & Lai, Shaoyong, 2011. "Exact computation of bivariate projection depth and the Stahel-Donoho estimator," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1173-1179, March.
    2. Rousseeuw, Peter J., 1993. "A resampling design for computing high-breakdown regression," Statistics & Probability Letters, Elsevier, vol. 18(2), pages 125-128, September.
    3. Subhajit Dutta & Anil Ghosh, 2012. "On robust classification using projection depth," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 657-676, June.
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    Cited by:

    1. Wei Shao & Yijun Zuo, 2020. "Computing the halfspace depth with multiple try algorithm and simulated annealing algorithm," Computational Statistics, Springer, vol. 35(1), pages 203-226, March.
    2. Dyckerhoff, Rainer & Mozharovskyi, Pavlo & Nagy, Stanislav, 2021. "Approximate computation of projection depths," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).

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