A0414
Title: Testing allometric extension in high-dimensional and spiked eigenvalue situations
Authors: Koji Tsukuda - Kyushu University (Japan) [presenting]
Shun Matsuura - Keio University (Japan)
Abstract: In multivariate allometry, the first principal component vector of a covariance matrix is of interest sometimes. In particular, when there are two groups, if the first principal component vectors of the two groups have the same direction and the direction is identical to the difference of the mean vectors, then one group is called an allometric extension of the other group. Several studies have considered statistical hypothesis testing of the allometric extension. However, previous studies dealt with the cases where the dimension of observed variables is smaller than sample sizes, and have not supposed high-dimensional situations. Statistical procedures that are not justified under high-dimensional asymptotic regimes do not work in high-dimensional situations often. Therefore, we propose a high-dimensional test procedure for allometric extension; in particular, we show the asymptotic normality of the test statistic and the consistency of the test under a high-dimensional asymptotic regime with an assumption that eigenvalues of covariance matrices are spiked.
