A jacobian inequality for gradient maps on the sphere and its application to directional statistics

Tomonari Sei

研究成果: Article査読

2 被引用数 (Scopus)

抄録

In the field of optimal transport theory, an optimal map is known to be a gradient map of a potential function satisfying cost-convexity. In this article, the Jacobian determinant of a gradient map is shown to be log-concave with respect to a convex combination of the potential functions when the underlying manifold is the sphere and the cost function is the distance squared. As an application to statistics, a new family of probability densities on the sphere is defined in terms of cost-convex functions. The log-concave property of the likelihood function follows from the inequality.

本文言語English
ページ(範囲)2525-2542
ページ数18
ジャーナルCommunications in Statistics - Theory and Methods
42
14
DOI
出版ステータスPublished - 2013 7 18
外部発表はい

ASJC Scopus subject areas

  • 統計学および確率

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