IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v101y2010i8p1898-1901.html
   My bibliography  Save this article

On an asymptotically more efficient estimation of the single-index model

Author

Listed:
  • Chang, Ziqing
  • Xue, Liugen
  • Zhu, Lixing

Abstract

In this note, we revisit the single-index model with heteroscedastic error, and recommend an estimating equation method in terms of transferring restricted least squares to unrestricted least squares: the estimator of the index parameter is asymptotically more efficient than existing estimators in the literature in the sense that it is of a smaller limiting variance.

Suggested Citation

  • Chang, Ziqing & Xue, Liugen & Zhu, Lixing, 2010. "On an asymptotically more efficient estimation of the single-index model," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1898-1901, September.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:8:p:1898-1901
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(10)00045-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Lixing Zhu & Liugen Xue, 2006. "Empirical likelihood confidence regions in a partially linear single‐index model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 549-570, June.
    2. Yu Y. & Ruppert D., 2002. "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1042-1054, December.
    3. Xia, Yingcun & Härdle, Wolfgang, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1162-1184, May.
    4. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    5. Xue, Liu-Gen & Zhu, Lixing, 2006. "Empirical likelihood for single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1295-1312, July.
    6. Hall, Peter & Yao, Qiwei, 2005. "Approximating conditional distribution functions using dimension reduction," LSE Research Online Documents on Economics 16333, London School of Economics and Political Science, LSE Library.
    7. Xia, Yingcun, 2006. "Asymptotic Distributions For Two Estimators Of The Single-Index Model," Econometric Theory, Cambridge University Press, vol. 22(6), pages 1112-1137, December.
    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. 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.
    2. Claudio Agostinelli & Ana M. Bianco & Graciela Boente, 2020. "Robust estimation in single-index models when the errors have a unimodal density with unknown nuisance parameter," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 855-893, June.
    3. Qihua Wang & Tao Zhang & Wolfgang Karl Härdle, 2016. "An Extended Single-index Model with Missing Response at Random," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(4), pages 1140-1152, December.
    4. Ke Wang & Dehui Wang, 2024. "Estimation for partially linear single-index spatial autoregressive model with covariate measurement errors," Statistical Papers, Springer, vol. 65(7), pages 4201-4241, September.
    5. Yang, Hu & Guo, Chaohui & Lv, Jing, 2014. "A robust and efficient estimation method for single-index varying-coefficient models," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 119-127.
    6. Huang, Zhensheng & Zhang, Riquan, 2011. "Efficient empirical-likelihood-based inferences for the single-index model," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 937-947, May.
    7. Lai, Peng & Wang, Qihua & Lian, Heng, 2012. "Bias-corrected GEE estimation and smooth-threshold GEE variable selection for single-index models with clustered data," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 422-432.
    8. Guo, Xu & Xu, Wangli & Zhu, Lixing, 2014. "Multi-index regression models with missing covariates at random," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 345-363.
    9. Yiping Yang & Tiejun Tong & Gaorong Li, 2019. "SIMEX estimation for single-index model with covariate measurement error," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(1), pages 137-161, March.

    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. Wu, Jingwei & Peng, Hanxiang & Tu, Wanzhu, 2019. "Large-sample estimation and inference in multivariate single-index models," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 382-396.
    2. Huang, Zhensheng & Zhang, Riquan, 2011. "Efficient empirical-likelihood-based inferences for the single-index model," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 937-947, May.
    3. Jianglin Fang & Wanrong Liu & Xuewen Lu, 2018. "Empirical likelihood for heteroscedastic partially linear single-index models with growing dimensional data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(3), pages 255-281, April.
    4. Jia Chen & Jiti Gao & Degui Li, 2013. "Estimation in Single-Index Panel Data Models with Heterogeneous Link Functions," Econometric Reviews, Taylor & Francis Journals, vol. 32(8), pages 928-955, November.
    5. Huang, Zhensheng & Pang, Zhen, 2012. "Corrected empirical likelihood inference for right-censored partially linear single-index model," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 276-284.
    6. Li, Gaorong & Zhu, Lixing & Xue, Liugen & Feng, Sanying, 2010. "Empirical likelihood inference in partially linear single-index models for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 718-732, March.
    7. Huang, Zhensheng & Pang, Zhen & Zhang, Riquan, 2013. "Adaptive profile-empirical-likelihood inferences for generalized single-index models," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 70-82.
    8. Feng, Sanying & Kong, Kaidi & Kong, Yinfei & Li, Gaorong & Wang, Zhaoliang, 2022. "Statistical inference of heterogeneous treatment effect based on single-index model," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    9. Xue, Liugen & Zhang, Jinghua, 2020. "Empirical likelihood for partially linear single-index models with missing observations," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    10. Guo, Xu & Xu, Wangli & Zhu, Lixing, 2014. "Multi-index regression models with missing covariates at random," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 345-363.
    11. Huang, Lei & Jiang, Hui & Wang, Huixia, 2019. "A novel partial-linear single-index model for time series data," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 110-122.
    12. Jia Chen & Jiti Gao & Degui Li, 2013. "Estimation in Partially Linear Single-Index Panel Data Models With Fixed Effects," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 315-330, July.
    13. Han, Zhong-Cheng & Lin, Jin-Guan & Zhao, Yan-Yong, 2020. "Adaptive semiparametric estimation for single index models with jumps," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    14. Jianhong Shi & Qian Yang & Xiongya Li & Weixing Song, 2017. "Effects of measurement error on a class of single-index varying coefficient regression models," Computational Statistics, Springer, vol. 32(3), pages 977-1001, September.
    15. Lai, Peng & Wang, Qihua & Lian, Heng, 2012. "Bias-corrected GEE estimation and smooth-threshold GEE variable selection for single-index models with clustered data," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 422-432.
    16. Zhang, Wenyang & Li, Degui & Xia, Yingcun, 2015. "Estimation in generalised varying-coefficient models with unspecified link functions," Journal of Econometrics, Elsevier, vol. 187(1), pages 238-255.
    17. Jun Zhang, 2021. "Estimation and variable selection for partial linear single-index distortion measurement errors models," Statistical Papers, Springer, vol. 62(2), pages 887-913, April.
    18. Yang, Jing & Tian, Guoliang & Lu, Fang & Lu, Xuewen, 2020. "Single-index modal regression via outer product gradients," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    19. Lexin Li & Liping Zhu & Lixing Zhu, 2011. "Inference on the primary parameter of interest with the aid of dimension reduction estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 59-80, January.
    20. Chaohua Dong & Jiti Gao & Dag Tjostheim, 2014. "Estimation for Single-index and Partially Linear Single-index Nonstationary Time Series Models," Monash Econometrics and Business Statistics Working Papers 7/14, Monash University, Department of Econometrics and Business Statistics.

    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:101:y:2010:i:8:p:1898-1901. 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.