IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v66y2014i1p121-140.html
   My bibliography  Save this article

Bias-corrected statistical inference for partially linear varying coefficient errors-in-variables models with restricted condition

Author

Listed:
  • Sanying Feng
  • Liugen Xue

Abstract

In this paper, we consider the statistical inference for the partially liner varying coefficient model with measurement error in the nonparametric part when some prior information about the parametric part is available. The prior information is expressed in the form of exact linear restrictions. Two types of local bias-corrected restricted profile least squares estimators of the parametric component and nonparametric component are conducted, and their asymptotic properties are also studied under some regularity conditions. Moreover, we compare the efficiency of the two kinds of parameter estimators under the criterion of Loẅner ordering. Finally, we develop a linear hypothesis test for the parametric component. Some simulation studies are conducted to examine the finite sample performance for the proposed method. A real dataset is analyzed for illustration. Copyright The Institute of Statistical Mathematics, Tokyo 2014

Suggested Citation

  • Sanying Feng & Liugen Xue, 2014. "Bias-corrected statistical inference for partially linear varying coefficient errors-in-variables models with restricted condition," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 121-140, February.
    • Handle: RePEc:spr:aistmt:v:66:y:2014:i:1:p:121-140
    DOI: 10.1007/s10463-013-0407-z
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10463-013-0407-z
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10463-013-0407-z?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. Xiuli Wang & Gaorong Li & Lu Lin, 2011. "Empirical likelihood inference for semi-parametric varying-coefficient partially linear EV models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(2), pages 171-185, March.
    2. Harrison, David Jr. & Rubinfeld, Daniel L., 1978. "Hedonic housing prices and the demand for clean air," Journal of Environmental Economics and Management, Elsevier, vol. 5(1), pages 81-102, March.
    3. Yingcun Xia, 2004. "Efficient estimation for semivarying-coefficient models," Biometrika, Biometrika Trust, vol. 91(3), pages 661-681, September.
    4. Hu, Xuemei & Wang, Zhizhong & Zhao, Zhiwei, 2009. "Empirical likelihood for semiparametric varying-coefficient partially linear errors-in-variables models," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1044-1052, April.
    5. Zhang, Weiwei & Li, Gaorong & Xue, Liugen, 2011. "Profile inference on partially linear varying-coefficient errors-in-variables models under restricted condition," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 3027-3040, November.
    6. Liang, Hua, 1999. "Errors in variables models," SFB 373 Discussion Papers 1999,77, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    7. You, Jinhong & Chen, Gemai, 2006. "Estimation of a semiparametric varying-coefficient partially linear errors-in-variables model," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 324-341, February.
    8. Li, Gaorong & Feng, Sanying & Peng, Heng, 2011. "A profile-type smoothed score function for a varying coefficient partially linear model," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 372-385, February.
    9. Li, Gaorong & Lin, Lu & Zhu, Lixing, 2012. "Empirical likelihood for a varying coefficient partially linear model with diverging number of parameters," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 85-111.
    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. Zhaoliang Wang & Liugen Xue & Gaorong Li & Fei Lu, 2019. "Spline estimator for ultra-high dimensional partially linear varying coefficient models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 657-677, June.
    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.
    3. Yan-Ting Xiao & Fu-Xiao Li, 2020. "Estimation in partially linear varying-coefficient errors-in-variables models with missing response variables," Computational Statistics, Springer, vol. 35(4), pages 1637-1658, December.
    4. Xu, Hong-Xia & Fan, Guo-Liang & Chen, Zhen-Long, 2017. "Hypothesis tests in partial linear errors-in-variables models with missing response," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 219-229.
    5. Ai-Ai Liu & Han-Ying Liang, 2017. "Jackknife empirical likelihood of error variance in partially linear varying-coefficient errors-in-variables models," Statistical Papers, Springer, vol. 58(1), pages 95-122, March.
    6. Zhensheng Huang & Xing Sun & Riquan Zhang, 2022. "Estimation for partially varying-coefficient single-index models with distorted measurement errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(2), pages 175-201, February.
    7. Weiming Yang & Yiping Yang, 2020. "Composite quantile regression estimation of linear error-in-variable models using instrumental variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(1), pages 1-16, January.

    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. Li, Yujie & Li, Gaorong & Lian, Heng & Tong, Tiejun, 2017. "Profile forward regression screening for ultra-high dimensional semiparametric varying coefficient partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 133-150.
    2. Yang, Yiping & Li, Gaorong & Peng, Heng, 2014. "Empirical likelihood of varying coefficient errors-in-variables models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 1-18.
    3. Yan-Ting Xiao & Fu-Xiao Li, 2020. "Estimation in partially linear varying-coefficient errors-in-variables models with missing response variables," Computational Statistics, Springer, vol. 35(4), pages 1637-1658, December.
    4. 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.
    5. Zhaoliang Wang & Liugen Xue & Gaorong Li & Fei Lu, 2019. "Spline estimator for ultra-high dimensional partially linear varying coefficient models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 657-677, June.
    6. Jianhong Shi & Fanrong Zhao, 2018. "Statistical inference for heteroscedastic semi-varying coefficient EV models under restricted condition," Statistical Papers, Springer, vol. 59(2), pages 487-511, June.
    7. Zhang, Jun & Feng, Zhenghui & Zhou, Bu, 2014. "A revisit to correlation analysis for distortion measurement error data," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 116-129.
    8. Mingqiu Wang & Peixin Zhao & Xiaoning Kang, 2020. "Structure identification for varying coefficient models with measurement errors based on kernel smoothing," Statistical Papers, Springer, vol. 61(5), pages 1841-1857, October.
    9. Bang-Qiang He & Xing-Jian Hong & Guo-Liang Fan, 2020. "Penalized empirical likelihood for partially linear errors-in-variables panel data models with fixed effects," Statistical Papers, Springer, vol. 61(6), pages 2351-2381, December.
    10. Zhang, Weiwei & Li, Gaorong & Xue, Liugen, 2011. "Profile inference on partially linear varying-coefficient errors-in-variables models under restricted condition," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 3027-3040, November.
    11. Fang Lu & Jing Yang & Xuewen Lu, 2022. "One-step oracle procedure for semi-parametric spatial autoregressive model and its empirical application to Boston housing price data," Empirical Economics, Springer, vol. 62(6), pages 2645-2671, June.
    12. Shen, Si-Lian & Cui, Jian-Ling & Mei, Chang-Lin & Wang, Chun-Wei, 2014. "Estimation and inference of semi-varying coefficient models with heteroscedastic errors," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 70-93.
    13. Huang, Zhensheng & Zhou, Zhangong & Jiang, Rong & Qian, Weimin & Zhang, Riquan, 2010. "Empirical likelihood based inference for semiparametric varying coefficient partially linear models with error-prone linear covariates," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 497-504, March.
    14. Zhensheng Huang & Xing Sun & Riquan Zhang, 2022. "Estimation for partially varying-coefficient single-index models with distorted measurement errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(2), pages 175-201, February.
    15. Li, Gaorong & Feng, Sanying & Peng, Heng, 2011. "A profile-type smoothed score function for a varying coefficient partially linear model," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 372-385, February.
    16. Wang, Kangning & Li, Shaomin & Sun, Xiaofei & Lin, Lu, 2019. "Modal regression statistical inference for longitudinal data semivarying coefficient models: Generalized estimating equations, empirical likelihood and variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 257-276.
    17. Tang, Linjun & Zhou, Zhangong & Wu, Changchun, 2013. "Testing the linear errors-in-variables model with randomly censored data," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 875-884.
    18. Peixin Zhao & Liugen Xue, 2011. "Variable selection for varying coefficient models with measurement errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(2), pages 231-245, September.
    19. Ai-Ai Liu & Han-Ying Liang, 2017. "Jackknife empirical likelihood of error variance in partially linear varying-coefficient errors-in-variables models," Statistical Papers, Springer, vol. 58(1), pages 95-122, March.
    20. Zhou, Ling & Lin, Huazhen & Chen, Kani & Liang, Hua, 2019. "Efficient estimation and computation of parameters and nonparametric functions in generalized semi/non-parametric regression models," Journal of Econometrics, Elsevier, vol. 213(2), pages 593-607.

    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:66:y:2014:i:1:p:121-140. 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.