  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.
