A Two Sample Test in High Dimensional Data
Muni S. Srivastava, Shota Katayama and Yutaka Kano
Abstract
In this paper we propose a test for testing the equality of the mean vectors of two groups with unequal
covariance matrices based on $N_{1}$ and $N_{2}$ independently distributed $p$-dimensional
observation vectors.
It will be assumed that $N_{1}$ observation vectors from the first group
are normally distributed with mean vector $\bm{\mu}_{1}$ and covariance matrix $\bm{\Sigma}_{1}$.
Similarly, the $N_{2}$ observation vectors from the second group are normally distributed with mean vector
$\bm{\mu}_{2}$ and covariance matrix $\bm{\Sigma}_{2}$.
We propose a test for testing the hypothesis that $\bm{\mu}_{1}=\bm{\mu}_{2}$.
This test is invariant under the group of $p\times p$ nonsingular diagonal matrices.
The asymptotic distribution is obtained as $(N_{1},N_{2},p)\to\infty$ and
$N_{1}/(N_{1}+N_{2})\to k \in (0,1)$
but $N_{1}/p$ and $N_{2}/p$ may go to zero or infinity.
It is compared with a recently proposed non-invariant test.
It is shown that the proposed test performs the best.
Paper
http://dx.doi.org/10.1016/j.jmva.2012.08.014
(Correction Note)
