Title: General notions of regression depth function,
Abstract: As a measure for the centrality of a point in a set of multivariate data,
statistical depth functions play important roles in multivariate analysis,
because one may conveniently construct descriptive as well as inferential
procedures relying on them. Many depth notions have been proposed in the
literature to fit to different applications. However, most of them are mainly
developed for the location setting. In this paper, we discuss the possibility
of extending some of them into the regression setting. A general concept of
regression depth function is also provided.