Improvement of Misclassification Rates of Classifying Objects under Box Cox Transformation and Bootstrap Approach

Abstract

Discrimination and classification rules are based on different types of assumptions. Also, all most statistical methods are based on some necessary assumptions. Parametric methods are the best choice if it follows all the underlying assumptions. When assumptions are violated, parametric approaches do not provide a better solution and nonparametric techniques are preferred. After Box-Cox transformation, when assumptions are satisfied , parametric methods provide fewer misclassification rates. With this problem in mind, our concern is to compare the classification accuracy of parametric and non-parametric approaches with the aid of Box-Cox transformation and Bootstrapping. We carried Support Vector Machines (SVMs) and different discrimination and classification rules to classify objects. The attention is to critically compare the SVMs with Linear discrimination Analysis (LDA), and Quadratic discrimination Analysis (QDA) for measuring the performance of these techniques before and after Box-Cox transformation using misclassification rates. From the apparent error rates, we observe that before Box-Cox transformation, SVMs perform better than existing classification techniques, on the other hand, after Box-Cox transformation, parametric techniques provide fewer misclassification rates compared to nonparametric method. We also investigated the performances of classification techniques using the Bootstrap approach and observed that Bootstrap-based classification techniques significantly reduce the classification error rate than the usual techniques of small samples. Thus, this paper proposes to apply classification techniques under the Bootstrap approach for classifying objects in case of small sample. A real and simulated datasets application is carried out to see the performance.