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The Kullback information criterion for mixture regression models

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  • Hafidi, Bezza
  • Mkhadri, Abdallah

Abstract

We consider the problem of jointly selecting the number of components and variables in finite mixture regression models. The classical model selection criterion, AIC or BIC, may not be satisfactory in this setting, especially when the sample size is small or the number of variables is large. Specifically, they fit too many components and retain too many variables. An alternative mixture regression criterion, called MRC, which simultaneously determines the number of components and variables in mixture regression models, was proposed by Naik et al. (2007). In the same setting, we propose a new information criterion, called , for the simultaneous determination of the number of components and predictors. is based on the Kullback symmetric divergence instead of the Kullback directed divergence used for MRC. We show that the new criterion performs well than MRC in a small simulation study.

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  • Hafidi, Bezza & Mkhadri, Abdallah, 2010. "The Kullback information criterion for mixture regression models," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 807-815, May.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:9-10:p:807-815
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    References listed on IDEAS

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    1. C. S. Wong & W. K. Li, 2000. "On a mixture autoregressive model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 95-115.
    2. Tadesse, Mahlet G. & Sha, Naijun & Vannucci, Marina, 2005. "Bayesian Variable Selection in Clustering High-Dimensional Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 602-617, June.
    3. Naik, Prasad A. & Shi, Peide & Tsai, Chih-Ling, 2007. "Extending the Akaike Information Criterion to Mixture Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 244-254, March.
    4. Hafidi, B. & Mkhadri, A., 2006. "A corrected Akaike criterion based on Kullback's symmetric divergence: applications in time series, multiple and multivariate regression," Computational Statistics & Data Analysis, Elsevier, vol. 50(6), pages 1524-1550, March.
    5. Robert Tibshirani & Guenther Walther & Trevor Hastie, 2001. "Estimating the number of clusters in a data set via the gap statistic," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 411-423.
    6. Cavanaugh, Joseph E., 1999. "A large-sample model selection criterion based on Kullback's symmetric divergence," Statistics & Probability Letters, Elsevier, vol. 42(4), pages 333-343, May.
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    Cited by:

    1. Liu, Mengque & Zhang, Qingzhao & Fang, Kuangnan & Ma, Shuangge, 2020. "Structured analysis of the high-dimensional FMR model," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    2. Nicolas Depraetere & Martina Vandebroek, 2014. "Order selection in finite mixtures of linear regressions," Statistical Papers, Springer, vol. 55(3), pages 871-911, August.
    3. Huiyu Mao & Fukang Zhu & Yan Cui, 2020. "A generalized mixture integer-valued GARCH model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(3), pages 527-552, September.

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