Akaike Information Criterion for Selecting Components of the Mean Vector in High Dimensional Data with Fewer Observations

The Akaike information criterion (AIC) has been successfully used in the literature in model selection when there are a small number of parameters p and a large number of observations N . The cases when p is large and close to N or when p > N have not been considered in the literature. In fact, when p is large and close to N , the available AIC does not perform well at all. We consider these cases in the context of finding the number of components of the mean vector that may be different from zero in one-sample multivariate analysis. In fact, we consider this problem in more generality by considering it as a growth curve model introduced in Rao (1959) and Potthoff and Roy (1964). Using simulation, it has been shown that the proposed AIC procedures perform well.