IDEAS home Printed from https://ideas.repec.org/p/cap/mpaper/092009.html
   My bibliography  Save this paper

LINEAR DISCRIMINANT RULES for HIGH-DIMENSIONAL CORRELATED DATA: ASYMPTOTIC and FINITE SAMPLE RESULTS

Author

Listed:
  • Pedro Duarte Silva

    (Faculdade de Economia e Gestão, Universidade Católica Portuguesa - Porto)

Abstract

A new class of linear discrimination rules, designed for problems with many correlated variables, is proposed. This proposal tries to incorporate the most important patterns revealed by the empirical correlations and accurately approximate the optimal Bayes rule as the number of variables increases. In order to achieve this goal, the new rules rely on covariance matrix estimates derived from Gaussian factor models with small intrinsic dimensionality. Asymptotic results, based on a analysis that allows the number of variables to grow faster than the number of observations, show that the worst possible expected error rate of the proposed rules converges to the error of the optimal Bayes rule when the postulated model is true, and to a slightly larger constant when this model is a close approximation to the data generating process. Simulation results suggest that, in the data conditions they were designed for, the new rules can clearly outperform both Fisher's and naive linear discriminant rules.

Suggested Citation

  • Pedro Duarte Silva, 2009. "LINEAR DISCRIMINANT RULES for HIGH-DIMENSIONAL CORRELATED DATA: ASYMPTOTIC and FINITE SAMPLE RESULTS," Working Papers de Gestão (Management Working Papers) 09, Católica Porto Business School, Universidade Católica Portuguesa.
    • Handle: RePEc:cap:mpaper:092009
    as

    Download full text from publisher

    File URL: http://www.feg.porto.ucp.pt/docentes/repec/WP/092009%20-%20Silva%20-%20Linear%20discriminant%20rules.pdf
    File Function: First version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dudoit S. & Fridlyand J. & Speed T. P, 2002. "Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 77-87, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kubokawa, Tatsuya & Srivastava, Muni S., 2008. "Estimation of the precision matrix of a singular Wishart distribution and its application in high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1906-1928, October.
    2. Hossain, Ahmed & Beyene, Joseph & Willan, Andrew R. & Hu, Pingzhao, 2009. "A flexible approximate likelihood ratio test for detecting differential expression in microarray data," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3685-3695, August.
    3. Luca Scrucca, 2014. "Graphical tools for model-based mixture discriminant analysis," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(2), pages 147-165, June.
    4. Bilin Zeng & Xuerong Meggie Wen & Lixing Zhu, 2017. "A link-free sparse group variable selection method for single-index model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(13), pages 2388-2400, October.
    5. J. Burez & D. Van Den Poel, 2005. "CRM at a Pay-TV Company: Using Analytical Models to Reduce Customer Attrition by Targeted Marketing for Subscription Services," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 05/348, Ghent University, Faculty of Economics and Business Administration.
    6. Won, Joong-Ho & Lim, Johan & Yu, Donghyeon & Kim, Byung Soo & Kim, Kyunga, 2014. "Monotone false discovery rate," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 86-93.
    7. Jan, Budczies & Kosztyla, Daniel & von Törne, Christian & Stenzinger, Albrecht & Darb-Esfahani, Silvia & Dietel, Manfred & Denkert, Carsten, 2014. "cancerclass: An R Package for Development and Validation of Diagnostic Tests from High-Dimensional Molecular Data," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 59(i01).
    8. Jianqing Fan & Yang Feng & Jiancheng Jiang & Xin Tong, 2016. "Feature Augmentation via Nonparametrics and Selection (FANS) in High-Dimensional Classification," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 275-287, March.
    9. Márton Gosztonyi & Csákné Filep Judit, 2022. "Profiling (Non-)Nascent Entrepreneurs in Hungary Based on Machine Learning Approaches," Sustainability, MDPI, vol. 14(6), pages 1-20, March.
    10. Wang, Tao & Xu, Pei-Rong & Zhu, Li-Xing, 2012. "Non-convex penalized estimation in high-dimensional models with single-index structure," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 221-235.
    11. Un Jung Lee & ShengLi Tzeng & Yu-Chuan Chen & James J Chen, 2017. "Development of Predictive Signatures for Treatment Selection in Precision Medicine," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 2(4), pages 83-88, August.
    12. Alan R Dabney & John D Storey, 2007. "Optimality Driven Nearest Centroid Classification from Genomic Data," PLOS ONE, Public Library of Science, vol. 2(10), pages 1-7, October.
    13. Zhao, Jianhua & Yu, Philip L.H. & Shi, Lei & Li, Shulan, 2012. "Separable linear discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4290-4300.
    14. Chakraborty, Sounak, 2009. "Simultaneous cancer classification and gene selection with Bayesian nearest neighbor method: An integrated approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1462-1474, February.
    15. Shaheena Bashir & Edward Carter, 2010. "Penalized multinomial mixture logit model," Computational Statistics, Springer, vol. 25(1), pages 121-141, March.
    16. Park, Junyong & Park, DoHwan, 2015. "Stein’s method in high dimensional classification and applications," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 110-125.
    17. Chakraborty, Sounak, 2009. "Bayesian binary kernel probit model for microarray based cancer classification and gene selection," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4198-4209, October.
    18. Kasim Adetayo & Lin Dan & Van Sanden Suzy & Clevert Djork-Arné & Bijnens Luc & Göhlmann Hinrich & Amaratunga Dhammika & Hochreiter Sepp & Shkedy Ziv & Talloen Willem, 2010. "Informative or Noninformative Calls for Gene Expression: A Latent Variable Approach," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 9(1), pages 1-31, January.
    19. Jiang Wenyu & Varma Sudhir & Simon Richard, 2008. "Calculating Confidence Intervals for Prediction Error in Microarray Classification Using Resampling," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 7(1), pages 1-22, March.
    20. Dong, Kai & Pang, Herbert & Tong, Tiejun & Genton, Marc G., 2016. "Shrinkage-based diagonal Hotelling’s tests for high-dimensional small sample size data," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 127-142.

    More about this item

    Keywords

    Discriminant Analysis; High Dimensionality; Expected Misclassification Rate; Min-Max Regret;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cap:mpaper:092009. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ricardo Goncalves (email available below). General contact details of provider: https://edirc.repec.org/data/feucppt.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.