IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v62y2021i6d10.1007_s00362-020-01212-1.html
   My bibliography  Save this article

Model averaging marginal regression for high dimensional conditional quantile prediction

Author

Listed:
  • Jingwen Tu

    (Chongqing University)

  • Hu Yang

    (Chongqing University)

  • Chaohui Guo

    (Chongqing University
    Chongqing Normal University)

  • Jing Lv

    (Southwest University)

Abstract

In this article, we propose a high dimensional semiparametric model average approach to predict the conditional quantile of the response variable. Firstly, we approximate the multivariate conditional quantile function by an affine combination of one-dimensional marginal conditional quantile functions which can be estimated by the local linear regression. Secondly, based on the estimated marginal quantile regression functions, a penalized quantile regression is proposed to estimate and select the significant model weights involved in the approximation. Under some mild conditions, we have established the asymptotic properties for both the parametric and nonparametric estimators. Finally, we evaluate the finite sample performance of the proposed procedure via simulations and a real data analysis.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:6:d:10.1007_s00362-020-01212-1
    DOI: 10.1007/s00362-020-01212-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-020-01212-1
    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/s00362-020-01212-1?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. Joel L. Horowitz, 1998. "Bootstrap Methods for Median Regression Models," Econometrica, Econometric Society, vol. 66(6), pages 1327-1352, November.
    2. Tang, Yanlin & Song, Xinyuan & Wang, Huixia Judy & Zhu, Zhongyi, 2013. "Variable selection in high-dimensional quantile varying coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 115-132.
    3. 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.
    4. Hai Wang & Xinjie Chen & Nancy Flournoy, 2016. "The focused information criterion for varying-coefficient partially linear measurement error models," Statistical Papers, Springer, vol. 57(1), pages 99-113, March.
    5. Lu, Xun & Su, Liangjun, 2015. "Jackknife model averaging for quantile regressions," Journal of Econometrics, Elsevier, vol. 188(1), pages 40-58.
    6. Jialiang Li & Xiaochao Xia & Weng Kee Wong & David Nott, 2018. "Varying‐coefficient semiparametric model averaging prediction," Biometrics, The International Biometric Society, vol. 74(4), pages 1417-1426, December.
    7. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258.
    8. Jia Chen & Degui Li & Oliver Linton & Zudi Lu, 2018. "Semiparametric Ultra-High Dimensional Model Averaging of Nonlinear Dynamic Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 919-932, April.
    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.
    10. Paolo Frumento & Matteo Bottai, 2016. "Parametric modeling of quantile regression coefficient functions," Biometrics, The International Biometric Society, vol. 72(1), pages 74-84, March.
    11. Horowitz, Joel L. & Lee, Sokbae, 2005. "Nonparametric Estimation of an Additive Quantile Regression Model," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1238-1249, December.
    12. 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.
    13. Fan, Jianqing & Feng, Yang & Song, Rui, 2011. "Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 544-557.
    14. Chen, Jia & Li, Degui & Linton, Oliver & Lu, Zudi, 2016. "Semiparametric dynamic portfolio choice with multiple conditioning variables," Journal of Econometrics, Elsevier, vol. 194(2), pages 309-318.
    15. Hansen, Bruce E., 2008. "Least-squares forecast averaging," Journal of Econometrics, Elsevier, vol. 146(2), pages 342-350, October.
    16. 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.
    17. 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.
    18. 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.
    19. Jason Abrevaya, 2001. "The effects of demographics and maternal behavior on the distribution of birth outcomes," Empirical Economics, Springer, vol. 26(1), pages 247-257.
    20. Jing Lv & Hu Yang & Chaohui Guo, 2016. "Erratum to: Smoothing combined generalized estimating equations in quantile partially linear additive models with longitudinal data," Computational Statistics, Springer, vol. 31(3), pages 1235-1235, September.
    21. 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.
    22. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    23. 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.
    24. Li, Degui & Linton, Oliver & Lu, Zudi, 2015. "A flexible semiparametric forecasting model for time series," Journal of Econometrics, Elsevier, vol. 187(1), pages 345-357.
    25. 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.
    26. Hansen, Bruce E. & Racine, Jeffrey S., 2012. "Jackknife model averaging," Journal of Econometrics, Elsevier, vol. 167(1), pages 38-46.
    27. 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.
    28. 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.
    29. 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. Fang, Fang & Li, Jialiang & Xia, Xiaochao, 2022. "Semiparametric model averaging prediction for dichotomous response," Journal of Econometrics, Elsevier, vol. 229(2), pages 219-245.
    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. 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.
    4. Jia Chen & Degui Li & Oliver Linton & Zudi Lu, 2015. "Semiparametric model averaging of ultra-high dimensional time series," CeMMAP working papers CWP62/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. 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).
    6. Guo, Chaohui & Lv, Jing & Wu, Jibo, 2021. "Composite quantile regression for ultra-high dimensional semiparametric model averaging," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    7. 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.
    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. Fang, Fang & Yu, Zhou, 2020. "Model averaging assisted sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    11. 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.
    12. Sun, Yuying & Hong, Yongmiao & Wang, Shouyang & Zhang, Xinyu, 2023. "Penalized time-varying model averaging," Journal of Econometrics, Elsevier, vol. 235(2), pages 1355-1377.
    13. 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.
    14. 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.
    15. 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.
    16. Haili Zhang & Guohua Zou, 2020. "Cross-Validation Model Averaging for Generalized Functional Linear Model," Econometrics, MDPI, vol. 8(1), pages 1-35, February.
    17. 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.
    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. 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.

    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:stpapr:v:62:y:2021:i:6:d:10.1007_s00362-020-01212-1. 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.