Behavior of Fréchet mean and Central Limit Theorems on spheres

11/05/2019
by   Do Tran, et al.
0

Jacobi fields are used to compute higher derivatives of the Fréchet function on spheres with absolutely continuous 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.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset

Sign in with Google

×

Use your Google Account to sign in to DeepAI

×

Consider DeepAI Pro