Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence rates of eigenvector empirical spectral distribution of
  large dimensional sample covariance matrix   The eigenvector Empirical Spectral Distribution (VESD) is adopted to
investigate the limiting behavior of eigenvectors and eigenvalues of covariance
matrices. In this paper, we shall show that the Kolmogorov distance between the
expected VESD of sample covariance matrix and the Mar\v{c}enko-Pastur
distribution function is of order $O(N^{-1/2})$. Given that data dimension $n$
to sample size $N$ ratio is bounded between 0 and 1, this convergence rate is
established under finite 10th moment condition of the underlying distribution.
It is also shown that, for any fixed $\eta>0$, the convergence rates of VESD
are $O(N^{-1/4})$ in probability and $O(N^{-1/4+\eta})$ almost surely,
requiring finite 8th moment of the underlying distribution.

1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg