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High-dimensional AIC in the growth curve model

Author

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  • Fujikoshi, Yasunori
  • Enomoto, Rie
  • Sakurai, Tetsuro

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.

Suggested Citation

  • Fujikoshi, Yasunori & Enomoto, Rie & Sakurai, Tetsuro, 2013. "High-dimensional AIC in the growth curve model," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 239-250.
    • Handle: RePEc:eee:jmvana:v:122:y:2013:i:c:p:239-250
    DOI: 10.1016/j.jmva.2013.07.006
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    References listed on IDEAS

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    1. Satoh, Kenichi & Kobayashi, Mika & Fujikoshi, Yasunori, 1997. "Variable Selection for the Growth Curve Model," Journal of Multivariate Analysis, Elsevier, vol. 60(2), pages 277-292, February.
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    Cited by:

    1. Imori, Shinpei & Rosen, Dietrich von, 2015. "Covariance components selection in high-dimensional growth curve model with random coefficients," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 86-94.
    2. Xu, Shiyun & Shao, Menglin & Qiao, Wenxuan & Shang, Pengjian, 2018. "Generalized AIC method based on higher-order moments and entropy of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 1127-1138.

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