IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v65y2013i2p237-267.html
   My bibliography  Save this article

Partial linear single index models with distortion measurement errors

Author

Listed:
  • Jun Zhang
  • Yao Yu
  • Li-Xing Zhu
  • Hua Liang

Abstract

We study partial linear single index models when the response and the covariates in the parametric part are measured with errors and distorted by unknown functions of commonly observable confounding variables, and propose a semiparametric covariate-adjusted estimation procedure. We apply the minimum average variance estimation method to estimate the parameters of interest. This is different from all existing covariate-adjusted methods in the literature. Asymptotic properties of the proposed estimators are established. Moreover, we also study variable selection by adopting the coordinate-independent sparse estimation to select all relevant but distorted covariates in the parametric part. We show that the resulting sparse estimators can exclude all irrelevant covariates with probability approaching one. A simulation study is conducted to evaluate the performance of the proposed methods and a real data set is analyzed for illustration. Copyright The Institute of Statistical Mathematics, Tokyo 2013

Suggested Citation

  • Jun Zhang & Yao Yu & Li-Xing Zhu & Hua Liang, 2013. "Partial linear single index models with distortion measurement errors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(2), pages 237-267, April.
    • Handle: RePEc:spr:aistmt:v:65:y:2013:i:2:p:237-267
    DOI: 10.1007/s10463-012-0371-z
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10463-012-0371-z
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10463-012-0371-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. 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.
    2. 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.
    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. 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.
    5. Lexin Li, 2007. "Sparse sufficient dimension reduction," Biometrika, Biometrika Trust, vol. 94(3), pages 603-613.
    6. Liang, Hua & Li, Runze, 2009. "Variable Selection for Partially Linear Models With Measurement Errors," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 234-248.
    7. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    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. Yang, Hu & Yang, Jing, 2014. "A robust and efficient estimation and variable selection method for partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 227-242.
    3. Zhao, Jingxin & Xie, Chuanlong, 2018. "A nonparametric test for covariate-adjusted models," Statistics & Probability Letters, Elsevier, vol. 133(C), pages 65-70.
    4. 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.
    5. 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.
    6. Xie, Chuanlong & Zhu, Lixing, 2019. "A goodness-of-fit test for variable-adjusted models," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 27-48.
    7. Zhang, Jun & Li, Gaorong & Feng, Zhenghui, 2015. "Checking the adequacy for a distortion errors-in-variables parametric regression model," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 52-64.
    8. 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.
    9. Yingli Pan & Wen Cai & Zhan Liu, 2022. "Inference for non-probability samples under high-dimensional covariate-adjusted superpopulation model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(4), pages 955-979, October.

    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. Lai, Peng & Wang, Qihua & Zhou, Xiao-Hua, 2014. "Variable selection and semiparametric efficient estimation for the heteroscedastic partially linear single-index model," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 241-256.
    2. Feng, Sanying & Xue, Liugen, 2015. "Model detection and estimation for single-index varying coefficient model," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 227-244.
    3. Lian, Heng & Liang, Hua, 2016. "Separation of linear and index covariates in partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 56-70.
    4. Yang, Hu & Yang, Jing, 2014. "A robust and efficient estimation and variable selection method for partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 227-242.
    5. Jun Zhang & Zhenghui Feng & Peirong Xu, 2015. "Estimating the conditional single-index error distribution with a partial linear mean regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 61-83, March.
    6. 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.
    7. repec:wyi:journl:002176 is not listed on IDEAS
    8. 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.
    9. Zhang, Jun & Feng, Zhenghui & Peng, Heng, 2018. "Estimation and hypothesis test for partial linear multiplicative models," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 87-103.
    10. Dong, Chaohua & Gao, Jiti & Linton, Oliver, 2023. "High dimensional semiparametric moment restriction models," Journal of Econometrics, Elsevier, vol. 232(2), pages 320-345.
    11. Qingming Zou & Zhongyi Zhu, 2014. "M-estimators for single-index model using B-spline," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(2), pages 225-246, February.
    12. Yazhao Lv & Riquan Zhang & Weihua Zhao & Jicai Liu, 2014. "Quantile regression and variable selection for the single-index model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(7), pages 1565-1577, July.
    13. Jun Zhang & Zhenghui Feng & Peirong Xu & Hua Liang, 2017. "Generalized varying coefficient partially linear measurement errors models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 97-120, February.
    14. 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.
    15. 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.
    16. Gueuning, Thomas & Claeskens, Gerda, 2016. "Confidence intervals for high-dimensional partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 13-29.
    17. 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.
    18. Germán Aneiros & Philippe Vieu, 2015. "Partial linear modelling with multi-functional covariates," Computational Statistics, Springer, vol. 30(3), pages 647-671, September.
    19. Ma, Shujie & Liang, Hua & Tsai, Chih-Ling, 2014. "Partially linear single index models for repeated measurements," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 354-375.
    20. Zhang, Hong-Fan, 2021. "Minimum Average Variance Estimation with group Lasso for the multivariate response Central Mean Subspace," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    21. Huang, Zhensheng & Lin, Bingqing & Feng, Fan & Pang, Zhen, 2013. "Efficient penalized estimating method in the partially varying-coefficient single-index model," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 189-200.

    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:65:y:2013:i:2:p:237-267. 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.