Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random matrix-improved estimation of covariance matrix distances   Given two sets $x_1^{(1)},\ldots,x_{n_1}^{(1)}$ and
$x_1^{(2)},\ldots,x_{n_2}^{(2)}\in\mathbb{R}^p$ (or $\mathbb{C}^p$) of random
vectors with zero mean and positive definite covariance matrices $C_1$ and
$C_2\in\mathbb{R}^{p\times p}$ (or $\mathbb{C}^{p\times p}$), respectively,
this article provides novel estimators for a wide range of distances between
$C_1$ and $C_2$ (along with divergences between some zero mean and covariance
$C_1$ or $C_2$ probability measures) of the form $\frac1p\sum_{i=1}^n
f(\lambda_i(C_1^{-1}C_2))$ (with $\lambda_i(X)$ the eigenvalues of matrix $X$).
These estimators are derived using recent advances in the field of random
matrix theory and are asymptotically consistent as $n_1,n_2,p\to\infty$ with
non trivial ratios $p/n_1<1$ and $p/n_2<1$ (the case $p/n_2>1$ is also
discussed). A first "generic" estimator, valid for a large set of $f$
functions, is provided under the form of a complex integral. Then, for a
selected set of $f$'s of practical interest (namely, $f(t)=t$, $f(t)=\log(t)$,
$f(t)=\log(1+st)$ and $f(t)=\log^2(t)$), a closed-form expression is provided.
Beside theoretical findings, simulation results suggest an outstanding
performance advantage for the proposed estimators when compared to the
classical "plug-in" estimator $\frac1p\sum_{i=1}^n f(\lambda_i(\hat
C_1^{-1}\hat C_2))$ (with $\hat
C_a=\frac1{n_a}\sum_{i=1}^{n_a}x_i^{(a)}x_i^{(a){\sf T}}$), and this even for
very small values of $n_1,n_2,p$.

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The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
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The categories of this paper are: eess
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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: 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
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph