A test for the mean vector with fewer observations than the dimension under non-normality

In this article, we consider the problem of testing that the mean vector in the model , where are random p-vectors, and zij are independently and identically distributed with finite four moments, ; that is need not be normally distributed. We shall assume that C is a pxp non-singular matrix, and there are fewer observations than the dimension, N<=p. We consider the test statistic where is the sample mean vector, S=(sij) is the sample covariance matrix, DS= diag and n=N-1. The asymptotic null and non-null distributions of the test statistic T are derived.