A study on discriminant analysis techniques applied to multivariate lognormal data

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Abstract
The purpose of this paper is to examine the multiple group (>2) discrimination problem in which the group sizes are unequal and the variables used in the classification are correlated with skewed distributions. Using statistical simulation based on data from a clinical study, we compare the performances, in terms of misclassification rates, of nine statistical discrimination methods. These methods are linear and quadratic discriminant analysis applied to untransformed data, rank transformed data, and inverse normal scores data, as well as fixed kernel discriminant analysis, variable kernel discriminant analysis, and variable kernel discriminant analysis applied to inverse normal scores data. It is found that the parametric methods with transformed data generally outperform the other methods, and the parametric methods applied to inverse normal scores usually outperform the parametric methods applied to rank transformed data. Although the kernel methods often have very biased estimates, the variable kernel method applied to inverse normal scores data provides considerable improvement in terms of total nonerror rate.