Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonasymptotic Gaussian Approximation for Inference with Stable Noise   The results of a series of theoretical studies are reported, examining the
convergence rate for different approximate representations of $\alpha$-stable
distributions. Although they play a key role in modelling random processes with
jumps and discontinuities, the use of $\alpha$-stable distributions in
inference often leads to analytically intractable problems. The LePage series,
which is a probabilistic representation employed in this work, is used to
transform an intractable, infinite-dimensional inference problem into a
conditionally Gaussian parametric problem. A major component of our approach is
the approximation of the tail of this series by a Gaussian random variable.
Standard statistical techniques, such as Expectation-Maximization, Markov chain
Monte Carlo, and Particle Filtering, can then be applied. In addition to the
asymptotic normality of the tail of this series, we establish explicit,
nonasymptotic bounds on the approximation error. Their proofs follow classical
Fourier-analytic arguments, using Ess\'{e}en's smoothing lemma. Specifically,
we consider the distance between the distributions of: $(i)$~the tail of the
series and an appropriate Gaussian; $(ii)$~the full series and the truncated
series; and $(iii)$~the full series and the truncated series with an added
Gaussian term. In all three cases, sharp bounds are established, and the
theoretical results are compared with the actual distances (computed
numerically) in specific examples of symmetric $\alpha$-stable distributions.
This analysis facilitates the selection of appropriate truncations in practice
and offers theoretical guarantees for the accuracy of resulting estimates. One
of the main conclusions obtained is that, for the purposes of inference, the
use of a truncated series together with an approximately Gaussian error term
has superior statistical properties and is likely a preferable choice in
practice.

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The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
37
The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
3
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: acc-phys
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The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph