865 research outputs found
Functional CLT for sample covariance matrices
Using Bernstein polynomial approximations, we prove the central limit theorem
for linear spectral statistics of sample covariance matrices, indexed by a set
of functions with continuous fourth order derivatives on an open interval
including , the support of the
Mar\u{c}enko--Pastur law. We also derive the explicit expressions for
asymptotic mean and covariance functions.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ250 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
On testing the equality of high dimensional mean vectors with unequal covariance matrices
In this article, we focus on the problem of testing the equality of several
high dimensional mean vectors with unequal covariance matrices. This is one of
the most important problem in multivariate statistical analysis and there have
been various tests proposed in the literature. Motivated by \citet{BaiS96E} and
\cite{ChenQ10T}, a test statistic is introduced and the asymptomatic
distributions under the null hypothesis as well as the alternative hypothesis
are given. In addition, it is compared with a test statistic recently proposed
by \cite{SrivastavaK13Ta}. It is shown that our test statistic performs much
better especially in the large dimensional case
A Note on Rate of Convergence in Probability to Semicircular Law
In the present paper, we prove that under the assumption of the finite sixth
moment for elements of a Wigner matrix, the convergence rate of its empirical
spectral distribution to the Wigner semicircular law in probability is
when the dimension tends to infinity.Comment: 13 page
Convergence of the empirical spectral distribution function of Beta matrices
Let ,
where and are two independent sample covariance
matrices with dimension and sample sizes and , respectively. This is
the so-called Beta matrix. In this paper, we focus on the limiting spectral
distribution function and the central limit theorem of linear spectral
statistics of . Especially, we do not require or
to be invertible. Namely, we can deal with the case where
and . Therefore, our results cover many important
applications which cannot be simply deduced from the corresponding results for
multivariate matrices.Comment: Published at http://dx.doi.org/10.3150/14-BEJ613 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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