Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Omnibus CLTs for Fr\'echet means and nonparametric inference on
  non-Euclidean spaces   Two central limit theorems for sample Fr\'echet means are derived, both
significant for nonparametric inference on non-Euclidean spaces. The first one,
Theorem 2.2, encompasses and improves upon most earlier CLTs on Fr\'echet means
and broadens the scope of the methodology beyond manifolds to diverse new
non-Euclidean data including those on certain stratified spaces which are
important in the study of phylogenetic trees. It does not require that the
underlying distribution $Q$ have a density, and applies to both intrinsic and
extrinsic analysis. The second theorem, Theorem 3.3, focuses on intrinsic means
on Riemannian manifolds of dimensions $d>2$ and breaks new ground by providing
a broad CLT without any of the earlier restrictive support assumptions. It
makes the statistically reasonable assumption of a somewhat smooth density of
$Q$. The excluded case of dimension $d=2$ proves to be an enigma, although the
first theorem does provide a CLT in this case as well under a support
restriction. Theorem 3.3 immediately applies to spheres $S^d$, $d>2$, which are
also of considerable importance in applications to axial spaces and to
landmarks based image analysis, as these spaces are quotients of spheres under
a Lie group $\mathcal G $ of isometries of $S^d$.

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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc