Isotonic regression and isotonic projection

TL;DR

This paper investigates the geometric properties of cones in Euclidean space that allow for isotonic metric projections, demonstrating that projections onto isotonic regression cones preserve coordinate-wise order.

Contribution

It characterizes cones with isotonic metric projections and shows that projections onto isotonic regression cones are also isotonic, advancing understanding of isotonic regression geometry.

Findings

Identifies cones with isotonic metric projections.

Proves projections onto isotonic regression cones are isotonic.

Enhances geometric understanding of isotonic regression.

Abstract

The note describes the cones in the Euclidean space admitting isotonic metric projection with respect to the coordinate-wise ordering. As a consequence it is showed that the metric projection onto the regression cone (the cone defined by the general isotonic regression problem) admits a projection which is isotonic with respect to the coordinate-wise ordering.