Statistical depth meets computational geometry: a short survey

TL;DR

This survey reviews the intersection of statistical depth concepts with computational geometry, highlighting algorithms for multivariate medians and depth contours developed through interdisciplinary collaboration.

Contribution

It summarizes recent advances in algorithms for statistical depth functions and multivariate medians using computational geometry techniques.

Findings

Algorithms for depth and median computation are efficient and geometrically motivated.

Computational geometry has significantly contributed to multivariate statistical analysis.

Interdisciplinary collaboration has advanced the development of statistical depth methods.

Abstract

During the past two decades there has been a lot of interest in developing statistical depth notions that generalize the univariate concept of ranking to multivariate data. The notion of depth has also been extended to regression models and functional data. However, computing such depth functions as well as their contours and deepest points is not trivial. Techniques of computational geometry appear to be well-suited for the development of such algorithms. Both the statistical and the computational geometry communities have done much work in this direction, often in close collaboration. We give a short survey of this work, focusing mainly on depth and multivariate medians, and end by listing some other areas of statistics where computational geometry has been of great help in constructing efficient algorithms.