On Affine Invariant $L_p$ Depth Classifiers based on an Adaptive Choice of $p$

Abstract: In this article, we use L$_p$ depth for classification of multivariate data, where the value of $p$ is chosen adaptively using observations from the training sample. While many depth based classifiers are constructed assuming elliptic symmetry of the underlying distributions, our proposed L$_p$ depth classifiers cater to a larger class of distributions. We establish Bayes risk consistency of these proposed classifiers under appropriate regularity conditions. Several simulated and benchmark data sets are analyzed to compare their finite sample performance with some existing parametric and nonparametric classifiers including those based on other notions of data depth.