IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v30y2021i3d10.1007_s11749-020-00731-1.html
   My bibliography  Save this article

Empirical likelihood inference for generalized additive partially linear models

Author

Listed:
  • Rong Liu

    (The University of Toledo)

  • Yichuan Zhao

    (Georgia State University)

Abstract

Generalized additive partially linear models enjoy the simplicity of GLMs and the flexibility of GAMs because they combine both parametric and nonparametric components. Based on spline-backfitted kernel estimator, we propose empirical likelihood (EL)-based pointwise confidence intervals and simultaneous confidence bands (SCBs) for the nonparametric component functions to make statistical inference. Simulation study strongly supports the asymptotic theory and shows that EL-based SCBs are much easier for implementation and have better performance than Wald-type SCBs. We apply the proposed method to a university retention study and provide SCBs for the effect of the students information.

Suggested Citation

  • Rong Liu & Yichuan Zhao, 2021. "Empirical likelihood inference for generalized additive partially linear models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 569-585, September.
    • Handle: RePEc:spr:testjl:v:30:y:2021:i:3:d:10.1007_s11749-020-00731-1
    DOI: 10.1007/s11749-020-00731-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-020-00731-1
    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/s11749-020-00731-1?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. Rong Liu & Lijian Yang & Wolfgang K. Härdle, 2013. "Oracally Efficient Two-Step Estimation of Generalized Additive Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 619-631, June.
    2. Lan Xue & Hua Liang, 2010. "Polynomial Spline Estimation for a Generalized Additive Coefficient Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(1), pages 26-46, March.
    3. Shujie Ma & Jeffrey S. Racine & Lijian Yang, 2015. "Spline Regression in the Presence of Categorical Predictors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(5), pages 705-717, August.
    4. Jing Wang & Lijian Yang, 2009. "Efficient and fast spline-backfitted kernel smoothing of additive models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(3), pages 663-690, September.
    5. Liu, Rong & Yang, Lijian, 2010. "Spline-Backfitted Kernel Smoothing Of Additive Coefficient Model," Econometric Theory, Cambridge University Press, vol. 26(1), pages 29-59, February.
    6. Shuzhuan Zheng & Rong Liu & Lijian Yang & Wolfgang K. Härdle, 2016. "Statistical inference for generalized additive models: simultaneous confidence corridors and variable selection," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(4), pages 607-626, December.
    7. Hua Liang & Yongsong Qin & Xinyu Zhang & David Ruppert, 2009. "Empirical Likelihood‐Based Inferences for Generalized Partially Linear Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 433-443, September.
    8. Yanqing Sun & Rajeshwari Sundaram & Yichuan Zhao, 2009. "Empirical Likelihood Inference for the Cox Model with Time‐dependent Coefficients via Local Partial Likelihood," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 444-462, September.
    9. Park, Byeong U. & Mammen, Enno & Härdle, Wolfgang & Borak, Szymon, 2009. "Time Series Modelling With Semiparametric Factor Dynamics," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 284-298.
    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. Hu, Lixia & Huang, Tao & You, Jinhong, 2019. "Two-step estimation of time-varying additive model for locally stationary time series," Computational Statistics & Data Analysis, Elsevier, vol. 130(C), pages 94-110.
    2. Li, Xinyi & Wang, Li & Nettleton, Dan, 2019. "Sparse model identification and learning for ultra-high-dimensional additive partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 204-228.
    3. Takuma Yoshida, 2021. "Additive models for extremal quantile regression with Pareto-type distributions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(1), pages 103-134, March.
    4. Patrick, Joshua D. & Harvill, Jane L. & Hansen, Clifford W., 2016. "A semiparametric spatio-temporal model for solar irradiance data," Renewable Energy, Elsevier, vol. 87(P1), pages 15-30.
    5. Boente, Graciela & Martínez, Alejandra Mercedes, 2023. "A robust spline approach in partially linear additive models," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    6. Shuzhuan Zheng & Rong Liu & Lijian Yang & Wolfgang K. Härdle, 2016. "Statistical inference for generalized additive models: simultaneous confidence corridors and variable selection," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(4), pages 607-626, December.
    7. Hu, Jianhua & You, Jinhong & Zhou, Xian, 2017. "Improved estimation of fixed effects panel data partially linear models with heteroscedastic errors," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 96-111.
    8. Georgios Gioldasis & Antonio Musolesi & Michel Simioni, 2020. "Model uncertainty, nonlinearities and out-of-sample comparison: evidence from international technology diffusion," Working Papers hal-02790523, HAL.
    9. Minggen Lu & Dana Loomis, 2013. "Spline-based semiparametric estimation of partially linear Poisson regression with single-index models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(4), pages 905-922, December.
    10. Joel L. Horowitz, 2012. "Nonparametric additive models," CeMMAP working papers CWP20/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Petra Burdejová & Wolfgang K. Härdle, 2019. "Dynamic semi-parametric factor model for functional expectiles," Computational Statistics, Springer, vol. 34(2), pages 489-502, June.
    12. Mestekemper, Thomas & Windmann, Michael & Kauermann, Göran, 2010. "Functional hourly forecasting of water temperature," International Journal of Forecasting, Elsevier, vol. 26(4), pages 684-699, October.
    13. Santiago Moreno-Bromberg & Luca Taschini, 2011. "Pollution permits, Strategic Trading and Dynamic Technology Adoption," Papers 1103.2914, arXiv.org.
    14. Daniel J. Henderson & Anne-Charlotte Souto & Le Wang, 2020. "Higher-Order Risk–Returns to Education," JRFM, MDPI, vol. 13(11), pages 1-25, October.
    15. Anand, Kartik & Gai, Prasanna & Marsili, Matteo, 2012. "Rollover risk, network structure and systemic financial crises," Journal of Economic Dynamics and Control, Elsevier, vol. 36(8), pages 1088-1100.
    16. Enzo Giacomini & Wolfgang Härdle & Volker Krätschmer, 2009. "Dynamic semiparametric factor models in risk neutral density estimation," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 93(4), pages 387-402, December.
    17. Eddie Anderson & Artem Prokhorov & Yajing Zhu, 2020. "A Simple Estimator of Two‐Dimensional Copulas, with Applications," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(6), pages 1375-1412, December.
    18. Stephan Stahlschmidt & Helmut Tausendteufel & Wolfgang K. Härdle, 2011. "Bayesian Networks and Sex-related Homicides," SFB 649 Discussion Papers SFB649DP2011-045, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    19. Mammen, Enno & Rothe, Christoph & Schienle, Melanie, 2016. "Semiparametric Estimation With Generated Covariates," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1140-1177, October.
    20. Li Cai & Lijie Gu & Qihua Wang & Suojin Wang, 2021. "Simultaneous confidence bands for nonparametric regression with missing covariate data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1249-1279, December.

    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:testjl:v:30:y:2021:i:3:d:10.1007_s11749-020-00731-1. 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.