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Corrected version of AIC for selecting multivariate normal linear regression models in a general nonnormal case

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  • Yanagihara, Hirokazu

Abstract

This paper deals with the bias reduction of Akaike information criterion (AIC) for selecting variables in multivariate normal linear regression models when the true distribution of observation is an unknown nonnormal distribution. We propose a corrected version of AIC which is partially constructed by the jackknife method and is adjusted to the exact unbiased estimator of the risk when the candidate model includes the true model. It is pointed out that the influence of nonnormality in the bias of our criterion is smaller than the ones in AIC and TIC. We verify that our criterion is better than the AIC, TIC and EIC by conducting numerical experiments.

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  • Yanagihara, Hirokazu, 2006. "Corrected version of AIC for selecting multivariate normal linear regression models in a general nonnormal case," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1070-1089, May.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:5:p:1070-1089
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    References listed on IDEAS

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    1. Yasunori Fujikoshi & Takafumi Noguchi & Megu Ohtaki & Hirokazu Yanagihara, 2003. "Corrected versions of cross-validation criteria for selecting multivariate regression and growth curve models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(3), pages 537-553, September.
    2. Makio Ishiguro & Yosiyuki Sakamoto & Genshiro Kitagawa, 1997. "Bootstrapping Log Likelihood and EIC, an Extension of AIC," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(3), pages 411-434, September.
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    Cited by:

    1. Cubadda, Gianluca & Guardabascio, Barbara & Hecq, Alain, 2017. "A vector heterogeneous autoregressive index model for realized volatility measures," International Journal of Forecasting, Elsevier, vol. 33(2), pages 337-344.
    2. Withers, Christopher S. & Nadarajah, Saralees, 2011. "Estimates of low bias for the multivariate normal," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1635-1647, November.
    3. Gianluca Cubadda & Alain Hecq & Sean Telg, 2019. "Detecting Co‐Movements in Non‐Causal Time Series," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 81(3), pages 697-715, June.
    4. Yanagihara, Hirokazu & Tonda, Tetsuji & Matsumoto, Chieko, 2006. "Bias correction of cross-validation criterion based on Kullback-Leibler information under a general condition," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 1965-1975, October.
    5. Christopher Withers & Saralees Nadarajah, 2013. "Calibration with low bias," Statistical Papers, Springer, vol. 54(2), pages 371-379, May.

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