Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large Covariance Estimation by Thresholding Principal Orthogonal
  Complements   This paper deals with the estimation of a high-dimensional covariance with a
conditional sparsity structure and fast-diverging eigenvalues. By assuming
sparse error covariance matrix in an approximate factor model, we allow for the
presence of some cross-sectional correlation even after taking out common but
unobservable factors. We introduce the Principal Orthogonal complEment
Thresholding (POET) method to explore such an approximate factor structure with
sparsity. The POET estimator includes the sample covariance matrix, the
factor-based covariance matrix (Fan, Fan, and Lv, 2008), the thresholding
estimator (Bickel and Levina, 2008) and the adaptive thresholding estimator
(Cai and Liu, 2011) as specific examples. We provide mathematical insights when
the factor analysis is approximately the same as the principal component
analysis for high-dimensional data. The rates of convergence of the sparse
residual covariance matrix and the conditional sparse covariance matrix are
studied under various norms. It is shown that the impact of estimating the
unknown factors vanishes as the dimensionality increases. The uniform rates of
convergence for the unobserved factors and their factor loadings are derived.
The asymptotic results are also verified by extensive simulation studies.
Finally, a real data application on portfolio allocation is presented.

31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg