High-dimensional AIC in the growth curve model

Yasunori Fujikoshi, Rie Enomoto and Tetsuro Sakurai

Journal of Multivariate Analysis, 2013, vol. 122, issue C, 239-250

Abstract: 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 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 our new criterion gives an estimator with small biases in a wide range of p and n. Next we derive 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.

Keywords: AIC; HAIC; Asymptotic distributions; High-dimensional criteria; Growth curve model (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:122:y:2013:i:c:p:239-250

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DOI: 10.1016/j.jmva.2013.07.006

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