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...

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...

This paper deals with the null distribution of a likelihood ratio (LR) statistic for testing the intraclass correlation structure. We derive an asymptotic expansion of the null distribution of the LR statistic when the number of variable p and the sample size N approach infinity together, while...

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,>

When two groups are present, they are said to form an allometric model, if one group is the extension of the other group along the main axis of variation. The model is widely used in the context of principal component analysis, especially for the description of growth processes of creatures. In...