A1410
Title: Asymptotic properties of multivariate depth quantiles
Authors: Giacomo Francisci - University of Trento (Italy) [presenting]
Abstract: Statistical depth functions describe the degree of centrality of a point with respect to a multivariate distribution and are an important tool in non-parametric and robust statistics. The point of maximum depth c defines the median of the distribution, whereas the level sets of the depth function are used to define multivariate quantiles. The quantile set at level a>0 may be identified with the radius function that assigns to every direction u in the unit sphere the greatest scalar s such that the depth of c+su is at least a. Under appropriate conditions, it is shown that the centered and rescaled radius function converges weakly in the space of bounded functions on the unit sphere to a Gaussian process and the covariance function is expressed in terms of the depth function. This result can be used to construct confidence regions and perform hypothesis testing for multivariate quantiles.
