Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Joint CLT for eigenvalue statistics from several dependent large
  dimensional sample covariance matrices with application   Let $\mathbf{X}_n=(x_{ij})$ be a $k \times n$ data matrix with
complex-valued, independent and standardized entries satisfying a
Lindeberg-type moment condition. We consider simultaneously $R$ sample
covariance matrices $\mathbf{B}_{nr}=\frac1n \mathbf{Q}_r \mathbf{X}_n
\mathbf{X}_n^*\mathbf{Q}_r^\top,~1\le r\le R$, where the $\mathbf{Q}_{r}$'s are
nonrandom real matrices with common dimensions $p\times k~(k\geq p)$. Assuming
that both the dimension $p$ and the sample size $n$ grow to infinity, the
limiting distributions of the eigenvalues of the matrices $\{\mathbf{B}_{nr}\}$
are identified, and as the main result of the paper, we establish a joint
central limit theorem for linear spectral statistics of the $R$ matrices
$\{\mathbf{B}_{nr}\}$. Next, this new CLT is applied to the problem of testing
a high dimensional white noise in time series modelling. In experiments the
derived test has a controlled size and is significantly faster than the
classical permutation test, though it does have lower power. This application
highlights the necessity of such joint CLT in the presence of several dependent
sample covariance matrices. In contrast, all the existing works on CLT for
linear spectral statistics of large sample covariance matrices deal with a
single sample covariance matrix ($R=1$).

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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci