Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hypothesis testing for eigenspaces of covariance matrix   Eigenspaces of covariance matrices play an important role in statistical
machine learning, arising in variety of modern algorithms. Quantitatively, it
is convenient to describe the eigenspaces in terms of spectral projectors. This
work focuses on hypothesis testing for the spectral projectors, both in one-
and two-sample scenario. We present new tests, based on a specific matrix norm
developed in order to utilize the structure of the spectral projectors. A new
resampling technique of independent interest is introduced and analyzed: it
serves as an alternative to the well-known multiplier bootstrap, significantly
reducing computational complexity of bootstrap-based methods. We provide
theoretical guarantees for the type-I error of our procedures, which remarkably
improve the previously obtained results in the field. Moreover, we analyze
power of our tests. Numerical experiments illustrate good performance of the
proposed methods compared to previously developed ones.

8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys