In this paper, a novel projection-based depth based on the Rayleigh quotient, Rayleigh projection depth (RPD), is proposed. Although, the traditional projection depth (PD) has many good properties, it is indeed not practical due to its difficult computation, especially for the high-dimensional...

In the present document, an extension of the statistical depth notion is introduced with the aim to allow for measuring proximities between pairs of points. In particular, we will extend the simplicial depth function, which measures how central is a point by using random simplices (triangles in...