The quarter median

TL;DR

This paper introduces a multivariate median based on quarter spaces, providing theoretical results on its existence, properties, and asymptotic behavior, expanding median concepts into higher dimensions.

Contribution

It presents a novel multivariate median using quarter spaces, with proofs of existence, equivariance, and asymptotic normality, advancing median theory in multivariate analysis.

Findings

Existence of the median established

Median exhibits equivariance properties

Asymptotic normality proven

Abstract

We introduce and discuss a multivariate version of the classical median that is based on an equipartition property with respect to quarter spaces. These arise as pairwise intersections of the half-spaces associated with the coordinate hyperplanes of an orthogonal basis. We obtain results on existence, equivariance, and asymptotic normality.