IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v73y2021i3d10.1007_s10463-020-00759-y.html
   My bibliography  Save this article

Model averaging for linear models with responses missing at random

Author

Listed:
  • Yuting Wei

    (University of Science and Technology of China)

  • Qihua Wang

    (Zhejiang Gongshang University
    Chinese Academy of Sciences)

  • Wei Liu

    (York University)

Abstract

In this paper, a model averaging approach is developed for the linear regression models with response missing at random. It is shown that the proposed method is asymptotically optimal in the sense of achieving the lowest possible squared error. A Monte Carlo study is conducted to investigate the finite sample performance of our proposal by comparing with some related methods, and the simulation results favor the proposed method. Moreover, a real data analysis is given to illustrate the practical application of our proposal.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:73:y:2021:i:3:d:10.1007_s10463-020-00759-y
    DOI: 10.1007/s10463-020-00759-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-020-00759-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10463-020-00759-y?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Qihua Wang & Yongjin Li, 2018. "How to Make Model†free Feature Screening Approaches for Full Data Applicable to the Case of Missing Response?," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(2), pages 324-346, June.
    2. 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.
    3. 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.
    4. Jiming Jiang & Thuan Nguyen & J. Sunil Rao, 2015. "The E-MS Algorithm: Model Selection With Incomplete Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1136-1147, September.
    5. Hjort N.L. & Claeskens G., 2003. "Frequentist Model Average Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 879-899, January.
    6. Qingfeng Liu & Ryo Okui, 2013. "Heteroscedasticity‐robust C(p) model averaging," Econometrics Journal, Royal Economic Society, vol. 16(3), pages 463-472, October.
    7. 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.
    8. Xinyu Zhang & Guohua Zou & Hua Liang, 2014. "Model averaging and weight choice in linear mixed-effects models," Biometrika, Biometrika Trust, vol. 101(1), pages 205-218.
    9. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    10. 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.
    11. Zhang, Xinyu, 2013. "Model averaging with covariates that are missing completely at random," Economics Letters, Elsevier, vol. 121(3), pages 360-363.
    12. Yang Y., 2001. "Adaptive Regression by Mixing," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 574-588, June.
    13. 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.
    14. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258, October.
    15. Ding, Xiaobo & Wang, Qihua, 2011. "Fusion-Refinement Procedure for Dimension Reduction With Missing Response at Random," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1193-1207.
    16. Hansen, Bruce E. & Racine, Jeffrey S., 2012. "Jackknife model averaging," Journal of Econometrics, Elsevier, vol. 167(1), pages 38-46.
    17. Schomaker, Michael & Wan, Alan T.K. & Heumann, Christian, 2010. "Frequentist Model Averaging with missing observations," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3336-3347, December.
    18. Xinyu Zhang & Alan Wan & Sherry Zhou, 2012. "Focused Information Criteria, Model Selection, and Model Averaging in a Tobit Model With a Nonzero Threshold," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 132-142.
    19. 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.
    20. Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, July.
    21. Zhimeng Sun & Zhi Su & Jingyi Ma, 2014. "Focused vector information criterion model selection and model averaging regression with missing response," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(3), pages 415-432, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Guozhi Hu & Weihu Cheng & Jie Zeng, 2023. "Optimal Model Averaging for Semiparametric Partially Linear Models with Censored Data," Mathematics, MDPI, vol. 11(3), pages 1-21, February.
    2. Jie Zeng & Weihu Cheng & Guozhi Hu, 2023. "Optimal Model Averaging Estimation for the Varying-Coefficient Partially Linear Models with Missing Responses," Mathematics, MDPI, vol. 11(8), pages 1-21, April.

    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. Wei, Yuting & Wang, Qihua, 2021. "Cross-validation-based model averaging in linear models with response missing at random," Statistics & Probability Letters, Elsevier, vol. 171(C).
    2. Zhang, Xinyu & Liu, Chu-An, 2023. "Model averaging prediction by K-fold cross-validation," Journal of Econometrics, Elsevier, vol. 235(1), pages 280-301.
    3. 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.
    4. 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.
    5. Fang, Fang & Li, Jialiang & Xia, Xiaochao, 2022. "Semiparametric model averaging prediction for dichotomous response," Journal of Econometrics, Elsevier, vol. 229(2), pages 219-245.
    6. Jingwen Tu & Hu Yang & Chaohui Guo & Jing Lv, 2021. "Model averaging marginal regression for high dimensional conditional quantile prediction," Statistical Papers, Springer, vol. 62(6), pages 2661-2689, December.
    7. 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).
    8. 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.
    9. Haili Zhang & Guohua Zou, 2020. "Cross-Validation Model Averaging for Generalized Functional Linear Model," Econometrics, MDPI, vol. 8(1), pages 1-35, February.
    10. 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.
    11. Lu, Xun & Su, Liangjun, 2015. "Jackknife model averaging for quantile regressions," Journal of Econometrics, Elsevier, vol. 188(1), pages 40-58.
    12. 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.
    13. 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.
    14. Qingfeng Liu & Ryo Okui & Arihiro Yoshimura, 2016. "Generalized Least Squares Model Averaging," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1692-1752, December.
    15. Christopher F. Parmeter & Alan T. K. Wan & Xinyu Zhang, 2019. "Model averaging estimators for the stochastic frontier model," Journal of Productivity Analysis, Springer, vol. 51(2), pages 91-103, June.
    16. 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.
    17. Zhang, Xiaomeng & Zhang, Xinyu, 2023. "Optimal model averaging based on forward-validation," Journal of Econometrics, Elsevier, vol. 237(2).
    18. Steven F. Lehrer & Tian Xie, 2022. "The Bigger Picture: Combining Econometrics with Analytics Improves Forecasts of Movie Success," Management Science, INFORMS, vol. 68(1), pages 189-210, January.
    19. Peng, Jingfu & Yang, Yuhong, 2022. "On improvability of model selection by model averaging," Journal of Econometrics, Elsevier, vol. 229(2), pages 246-262.
    20. Jie Zeng & Weihu Cheng & Guozhi Hu, 2023. "Optimal Model Averaging Estimation for the Varying-Coefficient Partially Linear Models with Missing Responses," Mathematics, MDPI, vol. 11(8), pages 1-21, April.

    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:spr:aistmt:v:73:y:2021:i:3:d:10.1007_s10463-020-00759-y. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.