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AIC for the non-concave penalized likelihood method

Author

Listed:
  • Yuta Umezu

    (Nagoya Institute of Technology)

  • Yusuke Shimizu

    (Josai University)

  • Hiroki Masuda

    (Kyushu University)

  • Yoshiyuki Ninomiya

    (Kyushu University)

Abstract

Non-concave penalized maximum likelihood methods are widely used because they are more efficient than the Lasso. They include a tuning parameter which controls a penalty level, and several information criteria have been developed for selecting it. While these criteria assure the model selection consistency, they have a problem in that there are no appropriate rules for choosing one from the class of information criteria satisfying such a preferred asymptotic property. In this paper, we derive an information criterion based on the original definition of the AIC by considering minimization of the prediction error rather than model selection consistency. Concretely speaking, we derive a function of the score statistic that is asymptotically equivalent to the non-concave penalized maximum likelihood estimator and then provide an estimator of the Kullback–Leibler divergence between the true distribution and the estimated distribution based on the function, whose bias converges in mean to zero.

Suggested Citation

  • Yuta Umezu & Yusuke Shimizu & Hiroki Masuda & Yoshiyuki Ninomiya, 2019. "AIC for the non-concave penalized likelihood method," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(2), pages 247-274, April.
    • Handle: RePEc:spr:aistmt:v:71:y:2019:i:2:d:10.1007_s10463-018-0649-x
    DOI: 10.1007/s10463-018-0649-x
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    References listed on IDEAS

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    Cited by:

    1. Junichiro Yoshida & Nakahiro Yoshida, 2024. "Quasi-maximum likelihood estimation and penalized estimation under non-standard conditions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(5), pages 711-763, October.
    2. Nakahiro Yoshida, 2022. "Quasi-likelihood analysis and its applications," Statistical Inference for Stochastic Processes, Springer, vol. 25(1), pages 43-60, April.
    3. Simon Clinet, 2020. "Quasi-likelihood analysis for marked point processes and application to marked Hawkes processes," Papers 2001.11624, arXiv.org, revised Aug 2021.
    4. Simon Clinet, 2022. "Quasi-likelihood analysis for marked point processes and application to marked Hawkes processes," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 189-225, July.
    5. Junichiro Yoshida & Nakahiro Yoshida, 2024. "Penalized estimation for non-identifiable models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(5), pages 765-796, October.

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