Convex Order Beyond Dimension One: Projection Tests, Counterexamples and Gaussian Mixtures VAJ9MBT3SJ

URI	`m2://res/VAJ9MBT3SJ`
Kind	preprint
Creators	Olivier Guéant
Date	2026-10-05
MSC	62-XX
Subjects	arxiv math.ST, arxiv q-fin.RM, arxiv stat.TH
Scope	in

Expressions

e1: version, preprint

Language	en
Date	2026-10-05
Ids	arXiv 2610.07404

Items in this resource

The mentions of the inventory that name this resource. Each name links to the card of its inventory row.

Item	Kind	Where	Source
A change of basis in dimension \(d=2\	statement	lemma 6	arxiv
Translated homogeneous test functions	statement	proposition 2	arxiv
Comparison with a two-component Gaussian mixture in dimension \(d=2\	statement	theorem 3	arxiv
Two-component Gaussian mixtures	statement	theorem 4	arxiv
A change of basis in arbitrary dimension	statement	proposition 10	arxiv
Threshold for one-dimensional projected convex order	statement	proposition 6	arxiv
A probability density	statement	lemma 4	arxiv
Boundary-support criterion	statement	lemma 1	arxiv
An absolutely continuous radial counterexample	statement	proposition 8	arxiv
Preservation under regularisation	statement	lemma 7	arxiv
One-dimensional projected convex order for radial distributions	statement	proposition 4	arxiv
One-dimensional projected convex order	definition	definition 1	arxiv
Radial counterexample in every dimension \(d\ge 2\	statement	theorem 2	arxiv
Threshold for multivariate convex order	statement	proposition 5	arxiv
Multivariate convex order for radial distributions	statement	proposition 3	arxiv
One-dimensional projected convex order is strictly weaker	statement	theorem 1	arxiv
Lipschitz convex test functions	statement	lemma 8	arxiv
Angular representation in the plane	statement	lemma 2	arxiv
Reduction to dimension \(d=2\	statement	lemma 5	arxiv
Homogeneous test functions for symmetric planar distributions	statement	proposition 1	arxiv
The normalised positive definite case	statement	proposition 9	arxiv
Convex order for real-valued random variables with symmetric distributions	statement	lemma 3	arxiv
Strict gap between the thresholds	statement	proposition 7	arxiv

Catalogue records

arxiv: 2610.07404 (work)
arxiv_text: 2610.07404 (work)