Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On optimal tests for rotational symmetry against new classes of
  hyperspherical distributions   Motivated by the central role played by rotationally symmetric distributions
in directional statistics, we consider the problem of testing rotational
symmetry on the hypersphere. We adopt a semiparametric approach and tackle
problems where the location of the symmetry axis is either specified or
unspecified. For each problem, we define two tests and study their asymptotic
properties under very mild conditions. We introduce two new classes of
directional distributions that extend the rotationally symmetric class and are
of independent interest. We prove that each test is locally asymptotically
maximin, in the Le Cam sense, for one kind of the alternatives given by the new
classes of distributions, both for specified and unspecified symmetry axis. The
tests, aimed to detect location-like and scatter-like alternatives, are
combined into convenient hybrid tests that are consistent against both
alternatives. We perform Monte Carlo experiments that illustrate the
finite-sample performances of the proposed tests and their agreement with the
asymptotic results. Finally, the practical relevance of our tests is
illustrated on a real data application from astronomy. The R package rotasym
implements the proposed tests and allows practitioners to reproduce the data
application.

34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th