Journal of Statistical and Econometric Methods

Some zero mean classification functions with unequal prior probabilities and non-normality

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• Abstract

  In this study, the problem of classifying a new observation vector into one of the known groups (π_i , i=1,2) distributed multivariate normal when the mean vectors are equal and the training data contaminated with outliers to be non-normal. Four classification rules are considered for equal and unequal prior probabilities and non-normality based on: Bartlett and Please method (BPM), Bayesian Posterior Probability Approach (BPP), the Quadratic Discriminant Function (QDF) and the Absolute Euclidean Distance Classifier method (AEDC). Female liked sex twins extracted from Stocks (1933) twin data is used for analysis and performance evaluation is based on Cross Validation (CV) and Balanced Error Rate (BER). While all four functions recorded higher error rates, BPM method was very sensitive to outliers. The QDF performed better with the least error rate under non-normality. BPM outperformed all the other classification rules under unequal prior probabilities. Similar results were obtained from the simulation study.