Recent advances in error rate estimation
Pattern Recognition Letters
Algorithms for Recognizing Contour-Traced Handprinted Characters
IEEE Transactions on Computers
Decorrelation of the true and estimated classifier errors in high-dimensional settings
EURASIP Journal on Bioinformatics and Systems Biology
On the relevance of linear discriminative features
Information Sciences: an International Journal
Noisy data elimination using mutual k-nearest neighbor for classification mining
Journal of Systems and Software
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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 particular, it applies in the small-sample settings commonly found in genomics and proteomics applications. Numerical examples, which include parameters estimated from actual microarray data, illustrate the analysis throughout.