Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Marchenko-Pastur Law for Tyler's M-estimator   This paper studies the limiting behavior of Tyler's M-estimator for the
scatter matrix, in the regime that the number of samples $n$ and their
dimension $p$ both go to infinity, and $p/n$ converges to a constant $y$ with
$0<y<1$. We prove that when the data samples $x_1, \ldots, x_n$ are identically
and independently generated from the Gaussian distribution $\mathcal{N}(0, I)$,
the operator norm of the difference between a properly scaled Tyler's
M-estimator and $\sum_{i=1}^n x_i x_i^\top/n$ tends to zero. As a result, the
spectral distribution of Tyler's M-estimator converges weakly to the
Mar\v{c}enko-Pastur distribution.

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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: cs