IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v50y2023i3p1325-1364.html
   My bibliography  Save this article

Frequentist model averaging for envelope models

Author

Listed:
  • Ziwen Gao
  • Jiahui Zou
  • Xinyu Zhang
  • Yanyuan Ma

Abstract

The envelope method produces efficient estimation in multivariate linear regression, and is widely applied in biology, psychology, and economics. This paper estimates parameters through a model averaging methodology and promotes the predicting abilities of the envelope models. We propose a frequentist model averaging method by minimizing a cross‐validation criterion. When all the candidate models are misspecified, the proposed model averaging estimator is proved to be asymptotically optimal. When correct candidate models exist, the coefficient estimator is proved to be consistent, and the sum of the weights assigned to the correct models, in probability, converges to one. Simulations and an empirical application demonstrate the effectiveness of the proposed method.

Suggested Citation

  • Ziwen Gao & Jiahui Zou & Xinyu Zhang & Yanyuan Ma, 2023. "Frequentist model averaging for envelope models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(3), pages 1325-1364, September.
    • Handle: RePEc:bla:scjsta:v:50:y:2023:i:3:p:1325-1364
    DOI: 10.1111/sjos.12634
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/sjos.12634
    Download Restriction: no
    File URL: https://libkey.io/10.1111/sjos.12634?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
    ---><---

    References listed on IDEAS

    as
    1. Yuan, Zheng & Yang, Yuhong, 2005. "Combining Linear Regression Models: When and How?," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1202-1214, December.
    2. Z. Su & G. Zhu & X. Chen & Y. Yang, 2016. "Sparse envelope model: efficient estimation and response variable selection in multivariate linear regression," Biometrika, Biometrika Trust, vol. 103(3), pages 579-593.
    3. A. Mukherjee & K. Chen & N. Wang & J. Zhu, 2015. "On the degrees of freedom of reduced-rank estimators in multivariate regression," Biometrika, Biometrika Trust, vol. 102(2), pages 457-477.
    4. Fang, Fang & Liu, Minhan, 2020. "Limit of the optimal weight in least squares model averaging with non-nested models," Economics Letters, Elsevier, vol. 196(C).
    5. R. Dennis Cook & Xin Zhang, 2015. "Foundations for Envelope Models and Methods," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 599-611, June.
    6. Lu, Xun & Su, Liangjun, 2015. "Jackknife model averaging for quantile regressions," Journal of Econometrics, Elsevier, vol. 188(1), pages 40-58.
    7. Yan Gao & Xinyu Zhang & Shouyang Wang & Terence Tai-leung Chong & Guohua Zou, 2019. "Frequentist model averaging for threshold models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(2), pages 275-306, April.
    8. Cheryl J. Flynn & Clifford M. Hurvich & Jeffrey S. Simonoff, 2013. "Efficiency for Regularization Parameter Selection in Penalized Likelihood Estimation of Misspecified Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 1031-1043, September.
    9. Gerda Claeskens & Christophe Croux & Johan Van Kerckhoven, 2006. "Variable Selection for Logistic Regression Using a Prediction-Focused Information Criterion," Biometrics, The International Biometric Society, vol. 62(4), pages 972-979, December.
    10. D. J. Eck & R. D. Cook, 2017. "Weighted envelope estimation to handle variability in model selection," Biometrika, Biometrika Trust, vol. 104(3), pages 743-749.
    11. Yuhong Yang, 2005. "Can the strengths of AIC and BIC be shared? A conflict between model indentification and regression estimation," Biometrika, Biometrika Trust, vol. 92(4), pages 937-950, December.
    12. Xie, Tian, 2015. "Prediction model averaging estimator," Economics Letters, Elsevier, vol. 131(C), pages 5-8.
    13. Zhihua Su & R. Dennis Cook, 2011. "Partial envelopes for efficient estimation in multivariate linear regression," Biometrika, Biometrika Trust, vol. 98(1), pages 133-146.
    14. Liu, Chu-An, 2015. "Distribution theory of the least squares averaging estimator," Journal of Econometrics, Elsevier, vol. 186(1), pages 142-159.
    15. Yang Y., 2001. "Adaptive Regression by Mixing," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 574-588, June.
    16. 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.
    17. Ganggang Xu & Suojin Wang & Jianhua Z. Huang, 2014. "Focused information criterion and model averaging based on weighted composite quantile regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 365-381, June.
    18. Hansen, Bruce E. & Racine, Jeffrey S., 2012. "Jackknife model averaging," Journal of Econometrics, Elsevier, vol. 167(1), pages 38-46.
    19. 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.
    20. 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. Zhang, Xinyu & Liu, Chu-An, 2023. "Model averaging prediction by K-fold cross-validation," Journal of Econometrics, Elsevier, vol. 235(1), pages 280-301.
    2. Zhang, Xiaomeng & Zhang, Xinyu, 2023. "Optimal model averaging based on forward-validation," Journal of Econometrics, Elsevier, vol. 237(2).
    3. Wenchao Xu & Xinyu Zhang, 2024. "On Asymptotic Optimality of Least Squares Model Averaging When True Model Is Included," Papers 2411.09258, arXiv.org.
    4. Chu-An Liu & Biing-Shen Kuo & Wen-Jen Tsay, 2017. "Autoregressive Spectral Averaging Estimator," IEAS Working Paper : academic research 17-A013, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    5. Shangwei Zhao & Jun Liao & Dalei Yu, 2020. "Model averaging estimator in ridge regression and its large sample properties," Statistical Papers, Springer, vol. 61(4), pages 1719-1739, August.
    6. 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.
    7. Ruoyao Shi, 2021. "An Averaging Estimator for Two Step M Estimation in Semiparametric Models," Working Papers 202105, University of California at Riverside, Department of Economics.
    8. Aman Ullah & Alan T. K. Wan & Huansha Wang & Xinyu Zhang & Guohua Zou, 2017. "A semiparametric generalized ridge estimator and link with model averaging," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 370-384, March.
    9. Xinyu Zhang & Dalei Yu & Guohua Zou & Hua Liang, 2016. "Optimal Model Averaging Estimation for Generalized Linear Models and Generalized Linear Mixed-Effects Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1775-1790, October.
    10. Haili Zhang & Guohua Zou, 2020. "Cross-Validation Model Averaging for Generalized Functional Linear Model," Econometrics, MDPI, vol. 8(1), pages 1-35, February.
    11. 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.
    12. 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, revised Jan 2023.
    13. Peng, Jingfu & Yang, Yuhong, 2022. "On improvability of model selection by model averaging," Journal of Econometrics, Elsevier, vol. 229(2), pages 246-262.
    14. Alena Skolkova, 2023. "Model Averaging with Ridge Regularization," CERGE-EI Working Papers wp758, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    15. Lu, Xun & Su, Liangjun, 2015. "Jackknife model averaging for quantile regressions," Journal of Econometrics, Elsevier, vol. 188(1), pages 40-58.
    16. Shou-Yung Yin & Chu-An Liu & Chang-Ching Lin, 2021. "Focused Information Criterion and Model Averaging for Large Panels With a Multifactor Error Structure," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(1), pages 54-68, January.
    17. Gao, Yan & Zhang, Xinyu & Wang, Shouyang & Zou, Guohua, 2016. "Model averaging based on leave-subject-out cross-validation," Journal of Econometrics, Elsevier, vol. 192(1), pages 139-151.
    18. 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).
    19. Xie, Tian, 2017. "Heteroscedasticity-robust model screening: A useful toolkit for model averaging in big data analytics," Economics Letters, Elsevier, vol. 151(C), pages 119-122.
    20. Chen, Xingyi & Li, Haiqi & Zhang, Jing, 2023. "Complete subset averaging approach for high-dimensional generalized linear models," Economics Letters, Elsevier, vol. 226(C).

    More about this item

    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:bla:scjsta:v:50:y:2023:i:3:p:1325-1364. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    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.