Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic Distributions for Likelihood Ratio Tests for the Equality of
  Covariance Matrices   Consider $k$ independent random samples from $p$-dimensional multivariate
normal distributions. We are interested in the limiting distribution of the
log-likelihood ratio test statistics for testing for the equality of $k$
covariance matrices. It is well known from classical multivariate statistics
that the limit is a chi-square distribution when $k$ and $p$ are fixed
integers. Jiang and Yang~\cite{JY13} and Jiang and Qi~\cite{JQ15} have obtained
the central limit theorem for the log-likelihood ratio test statistics when the
dimension $p$ goes to infinity with the sample sizes. In this paper, we derive
the central limit theorem when either $p$ or $k$ goes to infinity. We also
propose adjusted test statistics which can be well approximated by chi-squared
distributions regardless of values for $p$ and $k$. Furthermore, we present
numerical simulation results to evaluate the performance of our adjusted test
statistics and the log-likelihood ratio statistics based on classical
chi-square approximation and the normal approximation.

17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph