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

被引：0
作者：
Kento Egashira
Kazuyoshi Yata
Makoto Aoshima
机构：
[1] University of Tsukuba,Degree Programs in Pure and Applied Sciences, Graduate School of Science and Technology
[2] University of Tsukuba,Institute of Mathematics
来源：
Japanese Journal of Statistics and Data Science | 2021年 / 4卷
关键词：
Bias-corrected DWD; Discriminant analysis; HDLSS; Large ; small ; Weighted DWD;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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页码：821 / 840
页数：19
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