LINEAR DISCRIMINANT RULES for HIGH-DIMENSIONAL CORRELATED DATA: ASYMPTOTIC and FINITE SAMPLE RESULTS
AbstractA 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Faculdade de Economia e Gestão, Universidade Católica Portuguesa (Porto) in its series Working Papers de Gestão (Management Working Papers) with number 09.
Length: 17 pages
Date of creation: May 2009
Date of revision:
Discriminant Analysis; High Dimensionality; Expected Misclassification Rate; Min-Max Regret;
This paper has been announced in the following NEP Reports:
You can help add them by filling out this form.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ricardo Goncalves).
If references are entirely missing, you can add them using this form.