Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximum Likelihood Estimation for Linear Gaussian Covariance Models   We study parameter estimation in linear Gaussian covariance models, which are
$p$-dimensional Gaussian models with linear constraints on the covariance
matrix. Maximum likelihood estimation for this class of models leads to a
non-convex optimization problem which typically has many local maxima. Using
recent results on the asymptotic distribution of extreme eigenvalues of the
Wishart distribution, we provide sufficient conditions for any hill-climbing
method to converge to the global maximum. Although we are primarily interested
in the case in which $n>\!\!>p$, the proofs of our results utilize large-sample
asymptotic theory under the scheme $n/p \to \gamma > 1$. Remarkably, our
numerical simulations indicate that our results remain valid for $p$ as small
as $2$. An important consequence of this analysis is that for sample sizes $n
\simeq 14 p$, maximum likelihood estimation for linear Gaussian covariance
models behaves as if it were a convex optimization problem.

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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
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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: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat