The self-normalized Donsker theorem revisited

Abstract

We extend the Poincaré--Borel lemma to a weak approximation of a Brownian motion via simple functionals of uniform distributions on n-spheres in the Skorokhod space $D([0,1])$. This approach is used to simplify the proof of the self-normalized Donsker theorem in Csörgő et al. (2003). Some notes on spheres with respect to ${\ell }_p$-norms are given.

Published at http://dx.doi.org/10.15559/17-VMSTA82 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/)

References in corpus (1)

• Statistical analysis on high-dimensional spheres and shape spaces