Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Strong Convergence of the Optimal Linear Shrinkage Estimator for
  Large Dimensional Covariance Matrix   In this work we construct an optimal linear shrinkage estimator for the
covariance matrix in high dimensions. The recent results from the random matrix
theory allow us to find the asymptotic deterministic equivalents of the optimal
shrinkage intensities and estimate them consistently. The developed
distribution-free estimators obey almost surely the smallest Frobenius loss
over all linear shrinkage estimators for the covariance matrix. The case we
consider includes the number of variables $p\rightarrow\infty$ and the sample
size $n\rightarrow\infty$ so that $p/n\rightarrow c\in (0, +\infty)$.
Additionally, we prove that the Frobenius norm of the sample covariance matrix
tends almost surely to a deterministic quantity which can be consistently
estimated.

6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con