The logarithm map, its limits and Fréchet means in orthant spaces

Barden, D.; Le, Huiling

Abstract

The first part of the paper studies the expression for, and the properties of, the logarithm map on an orthant space, which is a simple stratified space, with the aim of analysing Fréchet means of probability measures on such a space. In the second part, we use these results to characterise Fréchet means and to derive various of their properties, including the limiting distribution of sample Fréchet means.

Citation

Barden, D., & Le, H. (2018). The logarithm map, its limits and Fréchet means in orthant spaces. Proceedings of the London Mathematical Society, 117(4), 751-789. https://doi.org/10.1112/plms.12149

• Journal Article Type: Article
• Acceptance Date: Apr 17, 2018
• Online Publication Date: Jun 13, 2018
• Publication Date: 2018-10
• Deposit Date: Apr 17, 2018
• Publicly Available Date: Jun 13, 2018
• Journal: Proceedings of the London Mathematical Society
• Print ISSN: 0024-6115
• Electronic ISSN: 1460-244X
• Publisher: London Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 117
• Issue: 4
• Pages: 751-789
• DOI: https://doi.org/10.1112/plms.12149
• Keywords: Fréchet mean; limiting distribution of sample Fréchet means; logarithm map; stratified space
• Public URL: https://nottingham-repository.worktribe.com/output/937550
• Publisher URL: https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/plms.12149