Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rapid evaluation of the spectral signal detection threshold and
  Stieltjes transform   Accurate detection of signal components is a frequently-encountered challenge
in statistical applications with low signal-to-noise ratio. This problem is
particularly challenging in settings with heteroscedastic noise. In certain
signal-plus-noise models of data, such as the classical spiked covariance model
and its variants, there are closed formulas for the spectral signal detection
threshold (the largest sample eigenvalue attributable solely to noise) for
isotropic noise in the limit of infinitely large data matrices. However, more
general noise models currently lack provably fast and accurate methods for
numerically evaluating the threshold.
  In this work, we introduce a rapid algorithm for evaluating the spectral
signal detection threshold in the limit of infinitely large data matrices. We
consider noise matrices with a separable variance profile (whose variance
matrix is rank one), as these arise often in applications. The solution is
based on nested applications of Newton's method. We also devise a new algorithm
for evaluating the Stieltjes transform of the spectral distribution at real
values exceeding the threshold. The Stieltjes transform on this domain is known
to be a key quantity in parameter estimation for spectral denoising methods.
The correctness of both algorithms is proven from a detailed analysis of the
master equations characterizing the Stieltjes transform, and their performance
is demonstrated in numerical experiments.

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The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
5
The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph