General notions of regression depth function

TL;DR

This paper explores extending statistical depth functions, traditionally used for data centrality in multivariate analysis, into the regression setting, proposing a general framework for regression depth functions.

Contribution

It introduces a general concept of regression depth functions, expanding the application of depth notions beyond location to regression analysis.

Findings

Proposes a unified framework for regression depth functions.

Discusses potential extensions of existing depth notions.

Lays groundwork for future regression depth methodologies.

Abstract

As a measure for the centrality of a point in a set of multivariate data, statistical depth functions play important roles in multivariate analysis, because one may conveniently construct descriptive as well as inferential procedures relying on them. Many depth notions have been proposed in the literature to fit to different applications. However, most of them are mainly developed for the location setting. In this paper, we discuss the possibility of extending some of them into the regression setting. A general concept of regression depth function is also provided.