Local depth

Local depth is a generalization of ordinary depth able to reveal local features of the probability distribution. Liu's simplicial depth is primarily used, but results for Tukey's halfspace depth are also derived. It is shown that the maximizers of local depth can help to detect the mode(s) of a probability distribution. This work is devoted to the univariate case, but the main definitions are stated in the general multivariate case. Theoretical results and applications are illustrated with several examples.