Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Lepski\u{i}-type stopping rule for the covariance estimation of
  multi-dimensional L\'evy processes   We suppose that a L\'evy process is observed at discrete time points.
Starting from an asymptotically minimax family of estimators for the continuous
part of the L\'evy Khinchine characteristics, i.e., the covariance, we derive a
data-driven parameter choice for the frequency of estimating the covariance. We
investigate a Lepski\u{i}-type stopping rule for the adaptive procedure.
Consequently, we use a balancing principle for the best possible data-driven
parameter. The adaptive estimator achieves almost the optimal rate. Numerical
experiments with the proposed selection rule are also presented.

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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
9
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: astro-ph
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex