Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fast, asymptotically efficient, recursive estimation in a Riemannian
  manifold   Stochastic optimisation in Riemannian manifolds, especially the Riemannian
stochastic gradient method, has attracted much recent attention. The present
work applies stochastic optimisation to the task of recursive estimation of a
statistical parameter which belongs to a Riemannian manifold. Roughly, this
task amounts to stochastic minimisation of a statistical divergence function.
The following problem is considered : how to obtain fast, asymptotically
efficient, recursive estimates, using a Riemannian stochastic optimisation
algorithm with decreasing step sizes? In solving this problem, several original
results are introduced. First, without any convexity assumptions on the
divergence function, it is proved that, with an adequate choice of step sizes,
the algorithm computes recursive estimates which achieve a fast non-asymptotic
rate of convergence. Second, the asymptotic normality of these recursive
estimates is proved, by employing a novel linearisation technique. Third, it is
proved that, when the Fisher information metric is used to guide the algorithm,
these recursive estimates achieve an optimal asymptotic rate of convergence, in
the sense that they become asymptotically efficient. These results, while
relatively familiar in the Euclidean context, are here formulated and proved
for the first time, in the Riemannian context. In addition, they are
illustrated with a numerical application to the recursive estimation of
elliptically contoured distributions.

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The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat