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http://hdl.handle.net/10397/88799
Title: | On the dimension effect of regularized linear discriminant analysis | Authors: | Wang, C Jiang, BY |
Issue Date: | 2018 | Source: | Electronic journal of statistics, 2018, , v. 12, no. 2, p. 2709-2742 | Abstract: | This paper studies the dimension effect of the linear discriminant analysis (LDA) and the regularized linear discriminant analysis (RLDA) classifiers for large dimensional data where the observation dimension p is of the same order as the sample size n. More specifically, built on properties of the Wishart distribution and recent results in random matrix theory, we derive explicit expressions for the asymptotic misclassification errors of LDA and RLDA respectively, from which we gain insights of how dimension affects the performance of classification and in what sense. Motivated by these results, we propose adjusted classifiers by correcting the bias brought by the unequal sample sizes. The bias-corrected LDA and RLDA classifiers are shown to have smaller misclassification rates than LDA and RLDA respectively. Several interesting examples are discussed in detail and the theoretical results on dimension effect are illustrated via extensive simulation studies. | Keywords: | Dimension effect Linear discriminant analysis Random matrix theory Regularized linear discriminant analysis |
Publisher: | Institute of Mathematical Statistics | Journal: | Electronic journal of statistics | EISSN: | 1935-7524 | DOI: | 10.1214/18-EJS1469 | Rights: | Electronic Journal of Statistics has chosen to apply the Creative Commons Attribution License (CCAL) to all articles we publish in this journal (click here to read the full-text legal codehttps://creativecommons.org/licenses/by/4.0/legalcode). Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles in EJS, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available. The following publication Wang, Cheng; Jiang, Binyan. On the dimension effect of regularized linear discriminant analysis. Electron. J. Statist. 12 (2018), no. 2, 2709--2742 is available at https://dx.doi.org/10.1214/18-EJS1469 |
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