Computing the Oja Median in R: The Package OjaNP

TL;DR

This paper reviews the properties of the Oja median, compares it with other multivariate medians, and introduces four algorithms for its computation, implemented in the R package OjaNP, along with related statistical tools.

Contribution

It introduces four algorithms for computing the Oja median and provides an R package with functions for related multivariate statistical analysis.

Findings

Algorithms enable practical computation of the Oja median.

The package includes tools for multivariate location tests.

Comparison highlights advantages and limitations of the Oja median.

Abstract

The Oja median is one of several extensions of the univariate median to the multivariate case. It has many nice properties, but is computationally demanding. In this paper, we first review the properties of the Oja median and compare it to other multivariate medians. Afterwards we discuss four algorithms to compute the Oja median, which are implemented in our R-package OjaNP. Besides these algorithms, the package contains also functions to compute Oja signs, Oja signed ranks, Oja ranks, and the related scatter concepts. To illustrate their use, the corresponding multivariate one- and $C$-sample location tests are implemented.