2019/11/05 by Tran, Do
#60F05 #62H11 #FOS: Mathematics #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.1911.01985
We compute higher derivatives of the Fréchet function on spheres with an absolutely continuous and rotationally symmetric probability distribution. Consequences include (i)~a practical condition to test if the mode of the symmetric distribution is a local Fréchet mean; (ii)~a Central Limit Theorem on spheres with practical assumptions and an explicit limiting distribution; and (iii)~an answer to the question of whether the smeary effect can occur on spheres with absolutely continuous and rotationally symmetric distributions: with the method presented here, it can in dimension at least~4.