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Adaptive Exponential Power Depth with Application to Classification

Author

Listed:
  • Yunlu Jiang

    (Jinan University)

  • Canhong Wen

    (Sun Yat-Sen University)

  • Xueqin Wang

    (Sun Yat-Sen University
    Sun Yat-Sen University
    Sun Yat-Sen University
    Sun Yat-Sen University)

Abstract

Depth functions have many applications in multivariate data analysis, including discriminant analysis and classification. In this paper, we introduce a novel class of data depth: exponential power depth (EPD) functions. Under some conditions, we show that the EPD functions are a statistical depth function, and the sample EPD functions are consistent and asymptotically normal. Based on the proposed EPD functions, we construct a DD-plot (depth-versus-depth plot), which can be applied to the classification problem. Since the EPD functions contain the two tuning parameters, we provide a data-driven approach to select these tuning parameters. The simulation studies and two real data analysis are conducted to assess the finite sample performance of the proposed method.

Suggested Citation

  • Yunlu Jiang & Canhong Wen & Xueqin Wang, 2018. "Adaptive Exponential Power Depth with Application to Classification," Journal of Classification, Springer;The Classification Society, vol. 35(3), pages 466-480, October.
    • Handle: RePEc:spr:jclass:v:35:y:2018:i:3:d:10.1007_s00357-018-9264-z
    DOI: 10.1007/s00357-018-9264-z
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    References listed on IDEAS

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    1. Yunlu Jiang & Shaoli Wang & Wenxiu Ge & Xueqin Wang, 2011. "Depth-based weighted empirical likelihood and general estimating equations," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 1051-1062.
    2. Cator, Eric A. & Lopuhaä, Hendrik P., 2010. "Asymptotic expansion of the minimum covariance determinant estimators," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2372-2388, November.
    3. Antonio Cuevas & Manuel Febrero & Ricardo Fraiman, 2007. "Robust estimation and classification for functional data via projection-based depth notions," Computational Statistics, Springer, vol. 22(3), pages 481-496, September.
    4. Jun Li & Juan A. Cuesta-Albertos & Regina Y. Liu, 2012. "DD -Classifier: Nonparametric Classification Procedure Based on DD -Plot," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 737-753, June.
    5. Croux, Christophe & Haesbroeck, Gentiane, 1999. "Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 161-190, November.
    6. 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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