DD -Classifier: Nonparametric Classification Procedure Based on DD -Plot

Using the DD -plot (depth vs. depth plot), we introduce a new nonparametric classification algorithm and call it DD -classifier. The algorithm is completely nonparametric, and it requires no prior knowledge of the underlying distributions or the form of the separating curve. Thus, it can be applied to a wide range of classification problems. The algorithm is completely data driven and its classification outcome can be easily visualized in a two-dimensional plot regardless of the dimension of the data. Moreover, it has the advantage of bypassing the estimation of underlying parameters such as means and scales, which is often required by the existing classification procedures. We study the asymptotic properties of the DD -classifier and its misclassification rate. Specifically, we show that DD -classifier is asymptotically equivalent to the Bayes rule under suitable conditions, and it can achieve Bayes error for a family broader than elliptical distributions. The performance of the classifier is also examined using simulated and real datasets. Overall, the DD -classifier performs well across a broad range of settings, and compares favorably with existing classifiers. It can also be robust against outliers or contamination.