Asymptotic properties of the misclassification rates for Euclidean Distance Discriminant rule in high-dimensional data

JOURNAL OF MULTIVARIATE ANALYSIS

卷:140

Article

Watanabe, Hiroki¹  Hyodo, Masashi²  Seo, Takashi¹  Pavlenko, Tatjana³ 

[1] Tokyo Univ Sci, Dept Math Informat Sci, Tokyo, Japan

[2] Osaka Prefecture Univ, Grad Sch Engn, Dept Math Sci, Sakai, Osaka, Japan

[3] KTH Royal Inst Technol, Dept Math, Stockholm, Sweden

关键词: High-dimensional framework;    Conditional error rate;    Expected error rate;   

DOI  :  10.1016/j.jmva.2015.05.008

来源: Elsevier

【 摘 要 】

Performance accuracy of the Euclidean Distance Discriminant rule (EDDR) is studied in the high-dimensional asymptotic framework which allows the dimensionality to exceed sample size. Under mild assumptions on the traces of the covariance matrix, our new results provide the asymptotic distribution of the conditional misclassification rate and the explicit expression for the consistent and asymptotically unbiased estimator of the expected misclassification rate. To get these properties, new results on the asymptotic normality of the quadratic forms and traces of the higher power of Wishart matrix, are established. Using our asymptotic results, we further develop two generic methods of determining a cut-off point for EDDR to adjust the misclassification rates. Finally, we numerically justify the high accuracy of our asymptotic findings along with the cut-off determination methods in finite sample applications, inclusive of the large sample and high-dimensional scenarios. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free