IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v126y2014icp100-113.html
   My bibliography  Save this article

Efficient estimation for partially linear varying coefficient models when coefficient functions have different smoothing variables

Author

Listed:
  • Yang, Seong J.
  • Park, Byeong U.

Abstract

In this paper we consider partially linear varying coefficient models. We provide semiparametric efficient estimators of the parametric part as well as rate-optimal estimators of the nonparametric part. In our model, different nonparametric coefficients have different smoothing variables. This requires employing a projection technique to get proper estimators of the nonparametric coefficients, and thus conventional kernel smoothing cannot give semiparametric efficient estimators of the parametric components. We take the smooth backfitting approach in conjunction with the profiling technique to get semiparametric efficient estimators of the parametric part. We also show that our estimators of the nonparametric part achieve the univariate rate of convergence, regardless of the covariate’s dimension. We report the finite sample properties of the semiparametric efficient estimators and compare them with those of other estimators.

Suggested Citation

  • Yang, Seong J. & Park, Byeong U., 2014. "Efficient estimation for partially linear varying coefficient models when coefficient functions have different smoothing variables," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 100-113.
    • Handle: RePEc:eee:jmvana:v:126:y:2014:i:c:p:100-113
    DOI: 10.1016/j.jmva.2014.01.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X14000128
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2014.01.004?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. Cai, Zongwu & Fan, Jianqing & Yao, Qiwei, 2000. "Functional-coefficient regression models for nonlinear time series," LSE Research Online Documents on Economics 6314, London School of Economics and Political Science, LSE Library.
    2. Zhao, Peixin & Xue, Liugen, 2010. "Variable selection for semiparametric varying coefficient partially linear errors-in-variables models," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1872-1883, September.
    3. Yang, Lijian & Park, Byeong U. & Xue, Lan & Hardle, Wolfgang, 2006. "Estimation and Testing for Varying Coefficients in Additive Models With Marginal Integration," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1212-1227, September.
    4. Xiaoke Zhang & Byeong U. Park & Jane-ling Wang, 2013. "Time-Varying Additive Models for Longitudinal Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 983-998, September.
    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. Byeong U. Park & Enno Mammen & Young K. Lee & Eun Ryung Lee, 2015. "Rejoinder," International Statistical Review, International Statistical Institute, vol. 83(1), pages 72-76, April.
    2. Fan, Guo-Liang & Liang, Han-Ying & Shen, Yu, 2016. "Penalized empirical likelihood for high-dimensional partially linear varying coefficient model with measurement errors," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 183-201.

    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. Lee, Kyeongeun & Lee, Young K. & Park, Byeong U. & Yang, Seong J., 2018. "Time-dynamic varying coefficient models for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 50-65.
    2. Xialu Liu & Zongwu Cai & Rong Chen, 2015. "Functional coefficient seasonal time series models with an application of Hawaii tourism data," Computational Statistics, Springer, vol. 30(3), pages 719-744, September.
    3. Tu, Yundong & Wang, Ying, 2022. "Spurious functional-coefficient regression models and robust inference with marginal integration," Journal of Econometrics, Elsevier, vol. 229(2), pages 396-421.
    4. Byeong U. Park & Enno Mammen & Young K. Lee & Eun Ryung Lee, 2015. "Varying Coefficient Regression Models: A Review and New Developments," International Statistical Review, International Statistical Institute, vol. 83(1), pages 36-64, April.
    5. Cai, Zongwu & Juhl, Ted & Yang, Bingduo, 2015. "Functional index coefficient models with variable selection," Journal of Econometrics, Elsevier, vol. 189(2), pages 272-284.
    6. Herwartz, H. & Xu, F., 2010. "A functional coefficient model view of the Feldstein-Horioka puzzle," Journal of International Money and Finance, Elsevier, vol. 29(1), pages 37-54, February.
    7. Delgado, Michael S. & McCloud, Nadine & Kumbhakar, Subal C., 2014. "A generalized empirical model of corruption, foreign direct investment, and growth," Journal of Macroeconomics, Elsevier, vol. 42(C), pages 298-316.
    8. Wong, Heung & Ip, Wai-cheung & Zhang, Riquan, 2008. "Varying-coefficient single-index model," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1458-1476, January.
    9. Sun, Zhihua & Ye, Xue & Sun, Liuquan, 2015. "Consistent test of error-in-variables partially linear model with auxiliary variables," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 118-131.
    10. E. Zacharias & T. Stengos, 2006. "Intertemporal pricing and price discrimination: a semiparametric hedonic analysis of the personal computer market," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(3), pages 371-386.
    11. Cai, Zongwu, 2003. "Nonparametric estimation equations for time series data," Statistics & Probability Letters, Elsevier, vol. 62(4), pages 379-390, May.
    12. Ying Wang & Peter C. B. Phillips & Yundong Tu, 2024. "Limit Theory and Inference in Non-cointegrated Functional Coefficient Regression," Cowles Foundation Discussion Papers 2399, Cowles Foundation for Research in Economics, Yale University.
    13. Wang, Qihua & Zhang, Riquan, 2009. "Statistical estimation in varying coefficient models with surrogate data and validation sampling," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2389-2405, November.
    14. Čížek, Pavel & Koo, Chao Hui, 2021. "Jump-preserving varying-coefficient models for nonlinear time series," Econometrics and Statistics, Elsevier, vol. 19(C), pages 58-96.
    15. Linton, Oliver & Xiao, Zhijie, 2019. "Efficient estimation of nonparametric regression in the presence of dynamic heteroskedasticity," Journal of Econometrics, Elsevier, vol. 213(2), pages 608-631.
    16. repec:hum:wpaper:sfb649dp2007-023 is not listed on IDEAS
    17. Hassani, Hossein & Yeganegi, Mohammad Reza & Gupta, Rangan, 2019. "Does inequality really matter in forecasting real housing returns of the United Kingdom?," International Economics, Elsevier, vol. 159(C), pages 18-25.
    18. Cai Zongwu & Chen Linna & Fang Ying, 2012. "A New Forecasting Model for USD/CNY Exchange Rate," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(3), pages 1-20, September.
    19. Olga Klopp & Marianna Pensky, 2013. "Sparse High-dimensional Varying Coefficient Model : Non-asymptotic Minimax Study," Working Papers 2013-30, Center for Research in Economics and Statistics.
    20. Kourtellos, Andros & Stengos, Thanasis & Sun, Yiguo, 2022. "Endogeneity In Semiparametric Threshold Regression," Econometric Theory, Cambridge University Press, vol. 38(3), pages 562-595, June.
    21. Heather L. R. Tierney, 2019. "Forecasting with the Nonparametric Exclusion-from-Core Inflation Persistence Model Using Real-Time Data," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 25(1), pages 39-63, February.

    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:eee:jmvana:v:126:y:2014:i:c:p:100-113. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.