Geometric quantile-based measures of multivariate distributional characteristics

TL;DR

This paper introduces new geometric quantile-based measures for multivariate distributional characteristics such as dispersion, skewness, kurtosis, and asymmetry, which are computationally simple and theoretically justified.

Contribution

The paper proposes novel geometric quantile-based measures for multivariate distributional features, providing theoretical support and practical experiments demonstrating their effectiveness.

Findings

Measures are easy to compute compared to volume-based methods

Experiments show measures effectively characterize distributional properties

Confidence regions with desired coverage are computed successfully

Abstract

Several new geometric quantile-based measures for multivariate dispersion, skewness, kurtosis, and spherical asymmetry are defined. These measures differ from existing measures, which use volumes and are easy to calculate. Some theoretical justification is given, followed by experiments illustrating that they are reasonable measures of these distributional characteristics and computing confidence regions with the desired coverage.