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Cross-validation for selecting the penalty factor in least squares model averaging

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  • Fang, Fang
  • Yang, Qiwei
  • Tian, Wenling

Abstract

Asymptotic properties of least squares model averaging have been discussed in the literature under two different scenarios: (i) all candidate models are under-fitted; and (ii) the candidate models include the true model and may also include over-fitted ones. The penalty factor ϕn in the weight selection criterion plays a critical role. Roughly speaking, ϕn=2 is usually preferred in the first scenario but it does not achieve asymptotic optimality in the second scenario as ϕn=log(n) does. It is difficult in the practice to select an appropriate penalty factor since the true scenario is unknown. We propose a non-trivial cross-validation procedure to select the penalty factor that leads to an asymptotically optimal estimator in an adaptive fashion for both scenarios.

Suggested Citation

  • Fang, Fang & Yang, Qiwei & Tian, Wenling, 2022. "Cross-validation for selecting the penalty factor in least squares model averaging," Economics Letters, Elsevier, vol. 217(C).
    • Handle: RePEc:eee:ecolet:v:217:y:2022:i:c:s0165176522002300
    DOI: 10.1016/j.econlet.2022.110683
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    References listed on IDEAS

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    1. Zhang, Xinyu, 2015. "Consistency of model averaging estimators," Economics Letters, Elsevier, vol. 130(C), pages 120-123.
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    6. Hansen, Bruce E. & Racine, Jeffrey S., 2012. "Jackknife model averaging," Journal of Econometrics, Elsevier, vol. 167(1), pages 38-46.
    7. Jialiang Li & Jing Lv & Alan T. K. Wan & Jun Liao, 2022. "AdaBoost Semiparametric Model Averaging Prediction for Multiple Categories," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(537), pages 495-509, January.
    8. Hao Zheng & Kam-Wah Tsui & Xiaoning Kang & Xinwei Deng, 2017. "Cholesky-based model averaging for covariance matrix estimation," Statistical Theory and Related Fields, Taylor & Francis Journals, vol. 1(1), pages 48-58, January.
    9. Rong Zhu & Alan T. K. Wan & Xinyu Zhang & Guohua Zou, 2019. "A Mallows-Type Model Averaging Estimator for the Varying-Coefficient Partially Linear Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 882-892, April.
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    Cited by:

    1. Chen, Xingyi & Li, Haiqi & Zhang, Jing, 2023. "Complete subset averaging approach for high-dimensional generalized linear models," Economics Letters, Elsevier, vol. 226(C).

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    More about this item

    Keywords

    Cross-validation; Frequentist model averaging; Linear models; Mallows model averaging;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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