Robust Depth-Based Inference in Elliptical Models

Abstract

Elliptical models are the most important family of multivariate probability distributions. We explore the properties of these distributions with respect to their halfspace depth and their illumination.

The densities of elliptically symmetric distributions are expressed only in terms of the depth, the illumination, and a univariate function that can be estimated from the data. These observations set the ground for robust and nonparametric inference for (nearly) elliptical models based on the use of depth and illumination.

Keywords

• Density estimation
• Elliptical distribution
• Halfspace depth
• Illumination