High-dimensional hypothesis testing for allometric extension model

Allometric extension model is a multivariate mixture model, in which two population distributions have a common first principal component vector of their covariance matrices and the direction of the difference of their mean vectors coincides with the first principal component vector. This paper studies hypothesis testing for the allometric extension model in a high-dimensional setting when the multivariate normal population distributions are assumed. A test statistic is constructed and its asymptotic normality is shown under the null hypothesis. The consistency of the test is discussed under the alternative hypothesis. Several numerical results on the size and power of the test are also presented.