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<p>This dissertation studies Central Limit Theorems (CLTs) of Frechet means on stratified
spaces. The broad goal of this work is to answer the following question: What information
one should expect to get by sampling from a stratified space? In particular, this
work explores relationships between geometry and different forms of CLT, namely classic,
smeary and sticky. The work starts with explicit forms of CLTs for spaces of constant
sectional curvature. As a consequence, we explain the effect of sectional curvature
on the behaviors of Frechet means. We then give a sufficient condition for a smeary
CLT to occur on spheres. In the later part, we propose a general form of CLT for star
shaped Riemannian stratified spaces. The general CLT we propose is universal in the
sense that it contains all of the different forms of aforementioned CLTs. The proposed
CLT is verified on manifolds and on any flat 2-dimensional spaces with an isolated
singularity.</p>
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