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Model averaging based on leave-subject-out cross-validation

Author

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  • Gao, Yan
  • Zhang, Xinyu
  • Wang, Shouyang
  • Zou, Guohua

Abstract

This paper develops a frequentist model averaging method based on the leave-subject-out cross-validation. This method is applicable not only to averaging longitudinal data models, but also to averaging time series models which can have heteroscedastic errors. The resulting model averaging estimators are proved to be asymptotically optimal in the sense of achieving the lowest possible squared errors. Both simulation study and empirical example show the superiority of the proposed estimators over their competitors.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:econom:v:192:y:2016:i:1:p:139-151
    DOI: 10.1016/j.jeconom.2015.07.006
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    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. Cheng, Xu & Hansen, Bruce E., 2015. "Forecasting with factor-augmented regression: A frequentist model averaging approach," Journal of Econometrics, Elsevier, vol. 186(2), pages 280-293.
    3. 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.
    4. Zhongyi Zhu & Wing K. Fung & Xuming He, 2008. "On the asymptotics of marginal regression splines with longitudinal data," Biometrika, Biometrika Trust, vol. 95(4), pages 907-917.
    5. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    6. Liu, Chu-An, 2015. "Distribution theory of the least squares averaging estimator," Journal of Econometrics, Elsevier, vol. 186(1), pages 142-159.
    7. Arellano, Manuel, 2003. "Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780199245291.
    8. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, September.
    9. Tomohiro Ando & Ker-Chau Li, 2014. "A Model-Averaging Approach for High-Dimensional Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 254-265, March.
    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. Yang Y., 2001. "Adaptive Regression by Mixing," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 574-588, June.
    12. Gerda Claeskens & Tatyana Krivobokova & Jean D. Opsomer, 2009. "Asymptotic properties of penalized spline estimators," Biometrika, Biometrika Trust, vol. 96(3), pages 529-544.
    13. 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.
    14. Lin D Y & Ying Z, 2001. "Semiparametric and Nonparametric Regression Analysis of Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 103-126, March.
    15. Welsh A.H. & Lin X. & Carroll R.J., 2002. "Marginal Longitudinal Nonparametric Regression: Locality and Efficiency of Spline and Kernel Methods," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 482-493, June.
    16. A. Antoniadis, 1997. "Wavelets in statistics: A review," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 6(2), pages 97-130, August.
    17. Jianqing Fan, 1997. "Comments on «Wavelets in statistics: A review» by A. Antoniadis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 6(2), pages 131-138, August.
    18. Hansen, Bruce E. & Racine, Jeffrey S., 2012. "Jackknife model averaging," Journal of Econometrics, Elsevier, vol. 167(1), pages 38-46.
    19. Liang, Hua & Zou, Guohua & Wan, Alan T. K. & Zhang, Xinyu, 2011. "Optimal Weight Choice for Frequentist Model Average Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1053-1066.
    20. 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.
    21. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, September.
    22. J. Fan & J.‐T. Zhang, 2000. "Two‐step estimation of functional linear models with applications to longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 303-322.
    23. Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, July.
    24. Inyoung Kim & Noah D. Cohen & Raymond J. Carroll, 2003. "Semiparametric Regression Splines in Matched Case-Control Studies," Biometrics, The International Biometric Society, vol. 59(4), pages 1158-1169, December.
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    Cited by:

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    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. Chen, Yi-Ting & Liu, Chu-An, 2023. "Model averaging for asymptotically optimal combined forecasts," Journal of Econometrics, Elsevier, vol. 235(2), pages 592-607.
    4. Sun, Yuying & Hong, Yongmiao & Wang, Shouyang & Zhang, Xinyu, 2023. "Penalized time-varying model averaging," Journal of Econometrics, Elsevier, vol. 235(2), pages 1355-1377.
    5. Zhao, Shangwei & Zhou, Jianhong & Li, Hongjun, 2016. "Model averaging with high-dimensional dependent data," Economics Letters, Elsevier, vol. 148(C), pages 68-71.
    6. Hui Xiao & Yiguo Sun, 2019. "On Tuning Parameter Selection in Model Selection and Model Averaging: A Monte Carlo Study," JRFM, MDPI, vol. 12(3), pages 1-16, June.
    7. 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.
    8. Haili Zhang & Guohua Zou, 2020. "Cross-Validation Model Averaging for Generalized Functional Linear Model," Econometrics, MDPI, vol. 8(1), pages 1-35, February.
    9. Michael Schomaker & Christian Heumann, 2020. "When and when not to use optimal model averaging," Statistical Papers, Springer, vol. 61(5), pages 2221-2240, October.
    10. Wang, Weiwei & Zhang, Qi & Zhang, Xinyu & Li, Xinmin, 2021. "Model averaging based on generalized method of moments," Economics Letters, Elsevier, vol. 200(C).
    11. 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).
    12. 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.
    13. Rongjie Jiang & Liming Wang & Yang Bai, 2021. "Optimal model averaging estimator for semi-functional partially linear models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(2), pages 167-194, February.
    14. 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.
    15. Liao, Jun & Zou, Guohua & Gao, Yan & Zhang, Xinyu, 2021. "Model averaging prediction for time series models with a diverging number of parameters," Journal of Econometrics, Elsevier, vol. 223(1), pages 190-221.
    16. Tao Huang & Jialiang Li, 2018. "Semiparametric model average prediction in panel data analysis," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(1), pages 125-144, January.
    17. Liao, Jun & Zou, Guohua, 2020. "Corrected Mallows criterion for model averaging," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    18. Liao, Jun & Zong, Xianpeng & Zhang, Xinyu & Zou, Guohua, 2019. "Model averaging based on leave-subject-out cross-validation for vector autoregressions," Journal of Econometrics, Elsevier, vol. 209(1), pages 35-60.
    19. Fang, Fang & Li, Jialiang & Xia, Xiaochao, 2022. "Semiparametric model averaging prediction for dichotomous response," Journal of Econometrics, Elsevier, vol. 229(2), pages 219-245.
    20. Zhang, Xiaomeng & Zhang, Xinyu, 2023. "Optimal model averaging based on forward-validation," Journal of Econometrics, Elsevier, vol. 237(2).
    21. Xiaochao Xia, 2021. "Model averaging prediction for nonparametric varying-coefficient models with B-spline smoothing," Statistical Papers, Springer, vol. 62(6), pages 2885-2905, December.
    22. Christian Brownlees & Vladislav Morozov, 2022. "Unit Averaging for Heterogeneous Panels," Papers 2210.14205, arXiv.org, revised May 2024.
    23. Greenaway-McGrevy, Ryan, 2022. "Forecast combination for VARs in large N and T panels," International Journal of Forecasting, Elsevier, vol. 38(1), pages 142-164.

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    More about this item

    Keywords

    Asymptotic optimality; Leave-subject-out cross-validation; Longitudinal data; Model averaging; Time series;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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