Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Consistent estimation of high-dimensional factor models when the factor
  number is over-estimated   A high-dimensional $r$-factor model for an $n$-dimensional vector time series
is characterised by the presence of a large eigengap (increasing with $n$)
between the $r$-th and the $(r+1)$-th largest eigenvalues of the covariance
matrix. Consequently, Principal Component (PC) analysis is the most popular
estimation method for factor models and its consistency, when $r$ is correctly
estimated, is well-established in the literature. However, popular factor
number estimators often suffer from the lack of an obvious eigengap in
empirical eigenvalues and tend to over-estimate $r$ due, for example, to the
existence of non-pervasive factors affecting only a subset of the series. We
show that the errors in the PC estimators resulting from the over-estimation of
$r$ are non-negligible, which in turn lead to the violation of the conditions
required for factor-based large covariance estimation. To remedy this, we
propose new estimators of the factor model based on scaling the entries of the
sample eigenvectors. We show both theoretically and numerically that the
proposed estimators successfully control for the over-estimation error, and
investigate their performance when applied to risk minimisation of a portfolio
of financial time series.

11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph