Several Robust Techniques In Two-Groups Unbiased Linear Classification - Okwonu, Friday Zinzendoff (2013)
The fundamental difficulty in classification problem is how to assign an observation accurately to the group it belongs. This thesis is written based on the limitations and weaknesses of the Fisher linear classification analysis and its robust version based on the minimum covariance determinant estimator. The Fisher’s procedure is not robust while the robust version depends upon information obtained from the half set. This study develops several techniques to address the weaknesses of the two methods. They are: M linear classification rule, filter linear classification rule, weighted linear classification rule and linear combination linear classification rule. These procedures are developed in such a way that the influential observations are modeled alongside the regular observations. The robustness and stability of these techniques depends on the separation parameters. Contamination models and control variables were used to investigate the classification performance of these linear classification rules. Classification difference was used to compare the classification performance of the proposed techniques over the Fisher linear classification analysis and the Fisher linear classification analysis based on the minimum covariance determinant procedures. The mean probability of correct classification for each procedure was used to compare the mean of the optimal probability of correct classification obtained from the uncontaminated data set in order to ascertain robustness, breakdown and admissibility of these techniques.