An empirical depth function for multivariate data

We introduce an empirical depth function for multivariate data based on the empirical likelihood ratio for the mean. This empirical depth function is defined through the empirical distribution of a sample. It is centred on the sample mean and has continuous, smooth and convex contours which capture the shape of the data points. We also show that there is an asymptotic equivalence between the empirical depth and the Mahalanobis depth.