IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v222y2025ics0167715225000513.html
   My bibliography  Save this article

Asymptotic optimality of generalized cross validation and regularized Mallows model averaging

Author

Listed:
  • Zou, Chenchen
  • Li, Xin
  • Li, Xinmin
  • Liang, Hua

Abstract

We propose a modified generalized cross-validation model averaging procedure for weight choice and prove the asymptotic optimality of the resultant estimators in the squared loss sense under much weaker assumptions than those imposed in the literature. The proposed model averaging can be regarded as an L2-regularized Mallows model averaging with varying coefficients. Furthermore, we propose a GCV-adjusted Mallows model averaging that achieves a faster convergence rate towards the optimal loss compared to using generalized cross-validation model averaging or Mallows model averaging individually. The performance of the proposed estimators is thoroughly evaluated through numerical experiments.

Suggested Citation

  • Zou, Chenchen & Li, Xin & Li, Xinmin & Liang, Hua, 2025. "Asymptotic optimality of generalized cross validation and regularized Mallows model averaging," Statistics & Probability Letters, Elsevier, vol. 222(C).
    • Handle: RePEc:eee:stapro:v:222:y:2025:i:c:s0167715225000513
    DOI: 10.1016/j.spl.2025.110406
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715225000513
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2025.110406?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Zhang, Xinyu, 2021. "A New Study On Asymptotic Optimality Of Least Squares Model Averaging," Econometric Theory, Cambridge University Press, vol. 37(2), pages 388-407, April.
    2. Fang, Fang & Yuan, Chaoxia & Tian, Wenling, 2023. "An Asymptotic Theory For Least Squares Model Averaging With Nested Models," Econometric Theory, Cambridge University Press, vol. 39(2), pages 412-441, April.
    3. Jan R. Magnus & Dmitry Danilov, 2004. "Forecast accuracy after pretesting with an application to the stock market," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(4), pages 251-274.
    4. Feng, Yang & Liu, Qingfeng & Okui, Ryo, 2020. "On the sparsity of Mallows model averaging estimator," Economics Letters, Elsevier, vol. 187(C).
    5. Zhang, Xinyu & Liu, Chu-An, 2023. "Model averaging prediction by K-fold cross-validation," Journal of Econometrics, Elsevier, vol. 235(1), pages 280-301.
    6. Xinyu Zhang & Guohua Zou & Hua Liang & Raymond J. Carroll, 2020. "Parsimonious Model Averaging With a Diverging Number of Parameters," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(530), pages 972-984, April.
    7. Zhang, Xinyu & Wan, Alan T.K. & Zou, Guohua, 2013. "Model averaging by jackknife criterion in models with dependent data," Journal of Econometrics, Elsevier, vol. 174(2), pages 82-94.
    8. Liao, Jun & Zou, Guohua, 2020. "Corrected Mallows criterion for model averaging," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    9. Wan, Alan T.K. & Zhang, Xinyu & Zou, Guohua, 2010. "Least squares model averaging by Mallows criterion," Journal of Econometrics, Elsevier, vol. 156(2), pages 277-283, June.
    10. Hansen, Bruce E. & Racine, Jeffrey S., 2012. "Jackknife model averaging," Journal of Econometrics, Elsevier, vol. 167(1), pages 38-46.
    11. Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wenchao Xu & Xinyu Zhang, 2024. "On Asymptotic Optimality of Least Squares Model Averaging When True Model Is Included," Papers 2411.09258, arXiv.org.
    2. Zhihao Zhao & Xinyu Zhang & Guohua Zou & Alan T. K. Wan & Geoffrey K. F. Tso, 2024. "Model averaging for estimating treatment effects," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(1), pages 73-92, February.
    3. Shi, Pengfei & Zhang, Xinyu & Zhong, Wei, 2024. "Estimating conditional average treatment effects with heteroscedasticity by model averaging and matching," Economics Letters, Elsevier, vol. 238(C).
    4. Zhao, Shangwei & Xie, Tian & Ai, Xin & Yang, Guangren & Zhang, Xinyu, 2023. "Correcting sample selection bias with model averaging for consumer demand forecasting," Economic Modelling, Elsevier, vol. 123(C).
    5. Liao, Jun & Wan, Alan T.K. & He, Shuyuan & Zou, Guohua, 2022. "Optimal model averaging for multivariate regression models," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    6. Yuan, Chaoxia & Fang, Fang & Ni, Lyu, 2022. "Mallows model averaging with effective model size in fragmentary data prediction," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    7. Zhongqi Liang & Caiya Zhang & Linjun Xu, 2024. "Model averaging for right censored data with measurement error," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 30(2), pages 501-527, April.
    8. Liao, Jun & Zou, Guohua, 2020. "Corrected Mallows criterion for model averaging," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    9. Yuting Wei & Qihua Wang & Wei Liu, 2021. "Model averaging for linear models with responses missing at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 535-553, June.
    10. Haowen Bao & Zongwu Cai & Yuying Sun & Shouyang Wang, 2023. "Penalized Model Averaging for High Dimensional Quantile Regressions," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202302, University of Kansas, Department of Economics.
    11. Qingfeng Liu & Andrey L. Vasnev, 2019. "A Combination Method for Averaging OLS and GLS Estimators," Econometrics, MDPI, vol. 7(3), pages 1-12, September.
    12. Zhang, Xiaomeng & Zhang, Xinyu, 2023. "Optimal model averaging based on forward-validation," Journal of Econometrics, Elsevier, vol. 237(2).
    13. Hongwei Zhang & Qiang He & Ben Jacobsen & Fuwei Jiang, 2020. "Forecasting stock returns with model uncertainty and parameter instability," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(5), pages 629-644, August.
    14. Wan, Alan T.K. & Zhang, Xinyu & Wang, Shouyang, 2014. "Frequentist model averaging for multinomial and ordered logit models," International Journal of Forecasting, Elsevier, vol. 30(1), pages 118-128.
    15. Yundong Tu & Siwei Wang, 2023. "Variable Screening and Model Averaging for Expectile Regressions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 85(3), pages 574-598, June.
    16. Yin-Wong Cheung & Wenhao Wang, 2020. "A Jackknife Model Averaging Analysis of RMB Misalignment Estimates," Journal of International Commerce, Economics and Policy (JICEP), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 1-45, June.
    17. Giuseppe Luca & Jan R. Magnus & Franco Peracchi, 2023. "Weighted-Average Least Squares (WALS): Confidence and Prediction Intervals," Computational Economics, Springer;Society for Computational Economics, vol. 61(4), pages 1637-1664, April.
    18. Lu, Xun & Su, Liangjun, 2015. "Jackknife model averaging for quantile regressions," Journal of Econometrics, Elsevier, vol. 188(1), pages 40-58.
    19. Sun, Yuying & Hong, Yongmiao & Lee, Tae-Hwy & Wang, Shouyang & Zhang, Xinyu, 2021. "Time-varying model averaging," Journal of Econometrics, Elsevier, vol. 222(2), pages 974-992.
    20. Liu, Chu-An, 2015. "Distribution theory of the least squares averaging estimator," Journal of Econometrics, Elsevier, vol. 186(1), pages 142-159.

    More about this item

    Keywords

    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:222:y:2025:i:c:s0167715225000513. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.