Asymptotic Expansion and Estimation of EPMC for Linear Classification Rules in High Dimension

Tatsuya Kubokawa, Masashi Hyodo and Muni S. Srivastava
Additional contact information
Tatsuya Kubokawa: Faculty of Economics, University of Tokyo
Masashi Hyodo: Graduate School of Economics, University of Tokyo
Muni S. Srivastava: Department of Statistics, University of Toronto,

No CIRJE-F-818, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: The problem of classifying a new observation vector into one of the two known groups distributed as multivariate normal with common covariance matrix is consid- ered. In this paper, we handle the situation that the dimension, p, of the observation vectors is less than the total number, N, of observation vectors from the two groups, but both p and N tend to in nity with the same order. Since the inverse of the sample covariance matrix is close to an ill condition in this situation, it may be better to replace it with the inverse of the ridge-type estimator of the covariance matrix in the linear discriminant analysis (LDA). The resulting rule is called the ridge-type linear discriminant analysis (RLDA). The second-order expansion of the expected probability of misclassi cation (EPMC) for RLDA is derived, and the second-order unbiased estimator of EMPC is given. These results not only provide the corresponding conclusions for LDA, but also clarify the condition that RLDA improves on LDA in terms of EPMC. Finally, the performances of the second-order approximation and the unbiased estimator are investigated by simulation.

Pages: 30 pages
Date: 2011-09
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.cirje.e.u-tokyo.ac.jp/research/dp/2011/2011cf818.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2011cf818

Access Statistics for this paper

More papers in CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo Contact information at EDIRC.
Bibliographic data for series maintained by CIRJE administrative office ().