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Joint sampling distribution between actual and estimated classification errors for linear discriminant analysis

8 years 10 months ago
Joint sampling distribution between actual and estimated classification errors for linear discriminant analysis
Error estimation must be used to find the accuracy of a designed classifier, an issue that is critical in biomarker discovery for disease diagnosis and prognosis in genomics and proteomics. This paper presents, for what is believed to be the first time, the analytical formulation for the joint sampling distribution of the actual and estimated errors of a classification rule. The analysis presented here concerns the Linear Discriminant Analysis (LDA) classification rule and the resubstitution and leave-one-out error estimators, under a general parametric Gaussian assumption. Exact results are provided in the univariate case, and a simple method is suggested to obtain an accurate approximation in the multivariate case. It is also shown how these results can be applied in the computation of condition bounds and the regression of the actual error, given the observed error estimate. In contrast to asymptotic results, the analysis presented here is applicable to finite training data. In par...
Amin Zollanvari, Ulisses Braga-Neto, Edward R. Dou
Added 22 May 2011
Updated 22 May 2011
Type Journal
Year 2010
Where TIT
Authors Amin Zollanvari, Ulisses Braga-Neto, Edward R. Dougherty
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