Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semiparametrically efficient rank-based inference for shape I. optimal
  rank-based tests for sphericity   We propose a class of rank-based procedures for testing that the shape matrix
$\mathbf{V}$ of an elliptical distribution (with unspecified center of
symmetry, scale and radial density) has some fixed value ${\mathbf{V}}_0$; this
includes, for ${\mathbf{V}}_0={\mathbf{I}}_k$, the problem of testing for
sphericity as an important particular case. The proposed tests are invariant
under translations, monotone radial transformations, rotations and reflections
with respect to the estimated center of symmetry. They are valid without any
moment assumption. For adequately chosen scores, they are locally
asymptotically maximin (in the Le Cam sense) at given radial densities. They
are strictly distribution-free when the center of symmetry is specified, and
asymptotically so when it must be estimated. The multivariate ranks used
throughout are those of the distances--in the metric associated with the null
value ${\mathbf{V}}_0$ of the shape matrix--between the observations and the
(estimated) center of the distribution. Local powers (against elliptical
alternatives) and asymptotic relative efficiencies (AREs) are derived with
respect to the adjusted Mauchly test (a modified version of the Gaussian
likelihood ratio procedure proposed by Muirhead and Waternaux [Biometrika 67
(1980) 31--43]) or, equivalently, with respect to (an extension of) the test
for sphericity introduced by John [Biometrika 58 (1971) 169--174]. For Gaussian
scores, these AREs are uniformly larger than one, irrespective of the actual
radial density. Necessary and/or sufficient conditions for consistency under
nonlocal, possibly nonelliptical alternatives are given. Finite sample
performances are investigated via a Monte Carlo study.

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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin