Test-based classification: A linkage between classification and statistical testing

The purpose of this article is to introduce a new classification methodology. The methodology uses a connection, which we uncover, between classification and testing, and is called Test-based classification. Although the main focus of this article is the binary classification with the univariate and the multivariate data, an extension to the multiclass classification is also covered. Several simulated and real data sets are used to demonstrate how this new methodology works. We argue that our new idea is competitive with the linear and quadratic discriminant analysis when the observed data are normally distributed, but it can outperform them when the data are not normally distributed. Lanchenbruch's holdout misclassification rate is used to judge the performance of classification.