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.