The AIC and its modifications have been proposed for selecting the degree in a polynomial growth curve model under a large-sample framework when the sample size n is large, but the dimension p is fixed. In this paper, first we propose a high-dimensional AIC (denoted by HAIC) which is an...

The AIC, the multivariate Cp and their modifications have been proposed for multivariate linear regression models under a large-sample framework when the sample size n is large, but the dimension p of the response variables is fixed. In this paper, first we propose a high-dimensional AIC...

This paper is concerned with the testing problem of generalized multivariate linear hypothesis for the mean in the growth curve model(GMANOVA). Our interest is the case in which the number of the observed points p is relatively large compared to the sample size N. Asymptotic expansions of the...

This paper examines asymptotic distributions of the canonical correlations between and with q<=p, based on a sample of size of N=n+1. The asymptotic distributions of the canonical correlations have been studied extensively when the dimensions q and p are fixed and the sample size N tends toward infinity. However, these approximations worsen when q or p is large in comparison to N. To overcome this weakness, this paper first derives asymptotic distributions of the canonical correlations under a high-dimensional framework such that q is fixed, m=n-p-->[infinity] and c=p/n--c0[set membership, variant][0,1), assuming that and have a joint (q+p)-variate normal distribution. An extended Fisher's z-transformation is proposed. Then, the asymptotic...</=p,>