Exact computation of bivariate projection depth and the Stahel-Donoho estimator

The idea of data depth provides a new and promising methodology for multivariate nonparametric analysis. Nevertheless, the computation of data depth and the depth function has remained as a very challenging problem which has hindered the methodology from becoming more prevailing in practice. The same is true for the powerful Stahel-Donoho (S-D) estimator. Here, we present an exact algorithm for the computation of the bivariate projection depth (PD) of data points and consequently of the S-D estimator.