High-dimensional in the growth curve model.

Abstract: The 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 is large, but the dimension is fixed. In this paper, first we propose a high-dimensional (denoted by ) which is an asymptotic unbiased estimator of the -type risk function defined by the expected log-predictive likelihood or equivalently the Kullback–Leibler information, under a high-dimensional framework such that . It is noted that our new criterion gives an estimator with small biases in a wide range of and . Next we derive asymptotic distributions of and 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. [Copyright &y& Elsevier]