The logarithm map, its limits and Fréchet means in orthant spaces - Barden, D.; Le, Huiling (London Mathematical Society, 2018)
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.