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Evaluation of Error Rate Estimators in Discriminant Analysis with Multivariate Binary Variables
American Journal of Theoretical and Applied Statistics
Volume 5, Issue 4, July 2016, Pages: 173-179
Received: Apr. 1, 2016; Accepted: Apr. 19, 2016; Published: Jun. 4, 2016
Author
Egbo Ikechukwu, Department of Mathematics, Alvan Ikoku Federal College of Education, Owerri, Nigeria
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Abstract
Classification problems often suffers from small samples in conjunction with large number of features, which makes error estimation problematic. When a sample is small, there is insufficient data to split the sample and the same data are used for both classifier design and error estimation. Error estimation can suffer from high variance, bias or both. The problem of choosing a suitable error estimator is exacerbated by the fact that estimation performance depends on the rule used to design the classifier, the feature-label distribution to which the classifier is to be applied and the sample size. This paper is concerned with evaluation of error rate estimators in two group discriminant analysis with multivariate binary variables. Behaviour of eight most commonly used estimators are compared and contrasted by mean of Monte Carlo Simulation. The criterion used for comparing those error rate estimators is sum squared error rate (SSE). Four experimental factors are considered for the simulation namely: the number of variables, the sample size relative to number of variables, the prior probability and the correlation between the variables in the populations. From the analysis carried out the estimators can be ranked as follows: DS, O, OS, U, R, JK, P and D.
Keywords
Discriminant Analysis, Error Rate, Monte Carlo Simulation, Error Rate Estimators
Egbo Ikechukwu, Evaluation of Error Rate Estimators in Discriminant Analysis with Multivariate Binary Variables, American Journal of Theoretical and Applied Statistics. Vol. 5, No. 4, 2016, pp. 173-179. doi: 10.11648/j.ajtas.20160504.12
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