IDEAS home Printed from https://ideas.repec.org/a/spr/alstar/v103y2019i1d10.1007_s10182-018-0327-6.html
   My bibliography  Save this article

SIMEX estimation for single-index model with covariate measurement error

Author

Listed:
  • Yiping Yang

    (Chongqing Technology and Business University)

  • Tiejun Tong

    (Hong Kong Baptist University)

  • Gaorong Li

    (Beijing University of Technology)

Abstract

In this paper, we consider the single-index measurement error model with mismeasured covariates in the nonparametric part. To solve the problem, we develop a simulation-extrapolation (SIMEX) algorithm based on the local linear smoother and the estimating equation. For the proposed SIMEX estimation, it is not needed to assume the distribution of the unobserved covariate. We transform the boundary of a unit ball in $${\mathbb {R}}^p$$ R p to the interior of a unit ball in $${\mathbb {R}}^{p-1}$$ R p - 1 by using the constraint $$\Vert \beta \Vert =1$$ ‖ β ‖ = 1 . The proposed SIMEX estimator of the index parameter is shown to be asymptotically normal under some regularity conditions. We also derive the asymptotic bias and variance of the estimator of the unknown link function. Finally, the performance of the proposed method is examined by simulation studies and is illustrated by a real data example.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:alstar:v:103:y:2019:i:1:d:10.1007_s10182-018-0327-6
    DOI: 10.1007/s10182-018-0327-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10182-018-0327-6
    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/s10182-018-0327-6?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. 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. Hardle, Wolfgang & Tsybakov, A. B., 1993. "How sensitive are average derivatives?," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 31-48, July.
    3. Pang, Zhen & Xue, Liugen, 2012. "Estimation for the single-index models with random effects," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1837-1853.
    4. 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.
    5. Delaigle, Aurore & Hall, Peter, 2008. "Using SIMEX for Smoothing-Parameter Choice in Errors-in-Variables Problems," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 280-287, March.
    6. Joel L. Horowitz & Marianthi Markatou, 1996. "Semiparametric Estimation of Regression Models for Panel Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(1), pages 145-168.
    7. William Horrace & Christopher Parmeter, 2011. "Semiparametric deconvolution with unknown error variance," Journal of Productivity Analysis, Springer, vol. 35(2), pages 129-141, April.
    8. Xue, Liu-Gen & Zhu, Lixing, 2006. "Empirical likelihood for single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1295-1312, July.
    9. John Staudenmayer & David Ruppert, 2004. "Local polynomial regression and simulation–extrapolation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 17-30, February.
    10. Hardle, Wolfgang & Tsybakov, A. B., 1993. "How sensitive are average derivatives?," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 31-48, July.
    11. Hua Liang, 2009. "Generalized partially linear mixed-effects models incorporating mismeasured covariates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(1), pages 27-46, March.
    12. Yang, Suigen & Xue, Liugen & Li, Gaorong, 2014. "Simultaneous confidence band for single-index random effects models with longitudinal data," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 6-14.
    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. Chen, Li-Pang, 2019. "Semiparametric estimation for cure survival model with left-truncated and right-censored data and covariate measurement error," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    2. 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.
    3. Shi, Jianhong & Zhang, Yujing & Yu, Ping & Song, Weixing, 2021. "SIMEX estimation in parametric modal regression with measurement error," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    4. Jun Zhang, 2021. "Model checking for multiplicative linear regression models with mixed estimators," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(3), pages 364-403, August.
    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.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    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. 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).
    7. 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.
    8. 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).
    9. 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.
    10. 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.
    11. Ichimura, Hidehiko & Todd, Petra E., 2007. "Implementing Nonparametric and Semiparametric Estimators," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 74, Elsevier.
    12. Xia, Yingcun & Härdle, Wolfgang Karl & Linton, Oliver, 2009. "Optimal smoothing for a computationally and statistically efficient single index estimator," SFB 649 Discussion Papers 2009-028, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    13. Girard, Stéphane & Guillou, Armelle & Stupfler, Gilles, 2013. "Frontier estimation with kernel regression on high order moments," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 172-189.
    14. Kim, Peter T. & Koo, Ja-Yong & Park, Heon Jin, 2004. "Sharp minimaxity and spherical deconvolution for super-smooth error distributions," Journal of Multivariate Analysis, Elsevier, vol. 90(2), pages 384-392, August.
    15. Véronique Flambard & Pierre Lasserre & Pierre Mohnen, 2007. "Snow removal auctions in Montreal: costs, informational rents, and procurement management," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 40(1), pages 245-277, February.
    16. Yang, Suigen & Xue, Liugen & Li, Gaorong, 2014. "Simultaneous confidence band for single-index random effects models with longitudinal data," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 6-14.
    17. Huybrechts F. Bindele & Ash Abebe & Karlene N. Meyer, 2018. "General rank-based estimation for regression single index models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(5), pages 1115-1146, October.
    18. Bravo, Francesco & Escanciano, Juan Carlos & Van Keilegom, Ingrid, 2015. "Wilks' Phenomenon in Two-Step Semiparametric Empirical Likelihood Inference," LIDAM Discussion Papers ISBA 2015016, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    19. 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.
    20. Almekinders, Geert J & Eijffinger, Sylvester C W, 1994. "Daily Bundesbank and Federal Reserve Interventions: Are They a Reaction to Changes in the Level and Volatility of the DM/$-Rate?," Empirical Economics, Springer, vol. 19(1), pages 111-130.

    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:alstar:v:103:y:2019:i:1:d:10.1007_s10182-018-0327-6. 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.