High-dimensional ^sub AIC^ in the growth curve model

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 pp is fixed. In this paper, first this paper proposes a high-dimensional AIC (denoted by HAIC) which is an asymptotic unbiased estimator of the AIC-type risk function defined by the expected log-predictive likelihood or equivalently the Kullback-Leibler information, under a high-dimensional framework such that p/n...c...[0,1). It is noted that the new criterion gives an estimator with small biases in a wide range of p and n. Next this paper derives asymptotic distributions of AIC and HAIC under the high-dimensional framework. Through a Monte Carlo simulation, we note that these new approximations are more accurate than the approximations based on a large-sample framework. (ProQuest: ... denotes formulae/symbols omitted.)