Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large sample correlation matrices: a comparison theorem and its
  applications   In this paper, we show that the diagonal of a high-dimensional sample
covariance matrix stemming from $n$ independent observations of a
$p$-dimensional time series with finite fourth moments can be approximated in
spectral norm by the diagonal of the population covariance matrix. We assume
that $n,p\to \infty$ with $p/n$ tending to a constant which might be positive
or zero. As applications, we provide an approximation of the sample correlation
matrix ${\mathbf R}$ and derive a variety of results for its eigenvalues. We
identify the limiting spectral distribution of ${\mathbf R}$ and construct an
estimator for the population correlation matrix and its eigenvalues. Finally,
the almost sure limits of the extreme eigenvalues of ${\mathbf R}$ in a
generalized spiked correlation model are analyzed.

27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat