Asymptotic properties of distance-weighted discrimination and its bias correction for high-dimension, low-sample-size data

• Kento Egashira

• Kazuyoshi Yata

• Makoto Aoshima

抄録

While distance-weighted discrimination (DWD) was proposed to improve the support vector machine in high-dimensional settings, it is known that the DWD is quite sensitive to the imbalanced ratio of sample sizes. In this paper, we study asymptotic properties of the DWD in high-dimension, low-sample-size (HDLSS) settings. We show that the DWD includes a huge bias caused by a heterogeneity of covariance matrices as well as sample imbalance. We propose a bias-corrected DWD (BC-DWD) and show that the BC-DWD can enjoy consistency properties about misclassification rates. We also consider the weighted DWD (WDWD) and propose an optimal choice of weights in the WDWD. Finally, we discuss performances of the BC-DWD and the WDWD with the optimal weights in numerical simulations and actual data analyses.

収録刊行物

• Japanese Journal of Statistics and Data Science

  Japanese Journal of Statistics and Data Science 4 (2), 821-840, 2021-08-09

  Springer Science and Business Media LLC

キーワード

• Computational Theory and Mathematics
• Statistics and Probability

詳細情報

• CRID: 1361415748544383232
• NII論文ID: 210000176902
• DOI: 10.1007/s42081-021-00135-x
• ISSN: 25208764
• ISSN: 25208756
• Web Site: https://link.springer.com/content/pdf/10.1007/s42081-021-00135-x.pdf
• Web Site: https://link.springer.com/article/10.1007/s42081-021-00135-x/fulltext.html
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