IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v88y2025i2d10.1007_s00184-024-00953-5.html
   My bibliography  Save this article

Right-censored nonparametric regression with measurement error

Author

Listed:
  • Dursun Aydın

    (Mugla Sitki Kocman University)

  • Ersin Yılmaz

    (Mugla Sitki Kocman University)

  • Nur Chamidah

    (Airlangga University)

  • Budi Lestari

    (The University of Jember)

  • I. Nyoman Budiantara

    (Sepuluh Nopember Institute of Technology)

Abstract

This study focuses on estimating a nonparametric regression model with right-censored data when the covariate is subject to measurement error. To achieve this goal, it is necessary to solve the problems of censorship and measurement error ignored by many researchers. Note that the presence of measurement errors causes biased and inconsistent parameter estimates. Moreover, non-parametric regression techniques cannot be applied directly to right-censored observations. In this context, we consider an updated response variable using the Buckley–James method (BJM), which is essentially based on the Kaplan–Meier estimator, to solve the censorship problem. Then the measurement error problem is handled using the kernel deconvolution method, which is a specialized tool to solve this problem. Accordingly, three denconvoluted estimators based on BJM are introduced using kernel smoothing, local polynomial smoothing, and B-spline techniques that incorporate both the updated response variable and kernel deconvolution.The performances of these estimators are compared in a detailed simulation study. In addition, a real-world data example is presented using the Covid-19 dataset.

Suggested Citation

  • Dursun Aydın & Ersin Yılmaz & Nur Chamidah & Budi Lestari & I. Nyoman Budiantara, 2025. "Right-censored nonparametric regression with measurement error," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 88(2), pages 183-214, February.
    • Handle: RePEc:spr:metrik:v:88:y:2025:i:2:d:10.1007_s00184-024-00953-5
    DOI: 10.1007/s00184-024-00953-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-024-00953-5
    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/s00184-024-00953-5?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. Michel Delecroix & Olivier Lopez & Valentin Patilea, 2008. "Nonlinear Censored Regression Using Synthetic Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(2), pages 248-265, June.
    2. Wang, Xiao-Feng & Wang, Bin, 2011. "Deconvolution Estimation in Measurement Error Models: The R Package decon," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 39(i10).
    3. Li, Tong & Vuong, Quang, 1998. "Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 139-165, May.
    4. Osman, Muhtarjan & Ghosh, Sujit K., 2012. "Nonparametric regression models for right-censored data using Bernstein polynomials," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 559-573.
    5. Salah Khardani & Mohamed Lemdani & Elias Ould Saïd, 2012. "On the strong uniform consistency of the mode estimator for censored time series," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(2), pages 229-241, February.
    Full references (including those not matched with items on IDEAS)

    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. Salah, Khardani & Yousri, Slaoui, 2019. "Nonparametric relative regression under random censorship model," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 116-122.
    2. Yao Luo & Peijun Sang & Ruli Xiao, 2024. "Order Statistics Approaches to Unobserved Heterogeneity in Auctions," Working Papers tecipa-776, University of Toronto, Department of Economics.
    3. Lamy, Laurent, 2012. "The econometrics of auctions with asymmetric anonymous bidders," Journal of Econometrics, Elsevier, vol. 167(1), pages 113-132.
    4. Ali Al-Sharadqah & Majid Mojirsheibani & William Pouliot, 2020. "On the performance of weighted bootstrapped kernel deconvolution density estimators," Statistical Papers, Springer, vol. 61(4), pages 1773-1798, August.
    5. Peter Hall & Tapabrata Maiti, 2009. "Deconvolution methods for non‐parametric inference in two‐level mixed models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 703-718, June.
    6. Kirill S. Evdokimov & Andrei Zeleneev, 2023. "Simple Estimation of Semiparametric Models with Measurement Errors," Papers 2306.14311, arXiv.org, revised Jan 2025.
    7. Manuel Arellano & Stéphane Bonhomme, 2012. "Identifying Distributional Characteristics in Random Coefficients Panel Data Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(3), pages 987-1020.
    8. D.A. Ioannides & D.P. Papanastassiou, 2001. "Estimating the Distribution Function of a Stationary Process Involving Measurement Errors," Statistical Inference for Stochastic Processes, Springer, vol. 4(2), pages 181-198, May.
    9. Talamakrouni, Majda & El Ghouch, Anouar & Van Keilegom, Ingrid, 2012. "Guided censored regression," LIDAM Discussion Papers ISBA 2012023, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Kato, Kengo & Sasaki, Yuya, 2018. "Uniform confidence bands in deconvolution with unknown error distribution," Journal of Econometrics, Elsevier, vol. 207(1), pages 129-161.
    11. Roy, Arkaprava & Sarkar, Abhra, 2023. "Bayesian semiparametric multivariate density deconvolution via stochastic rotation of replicates," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    12. Susan Athey & Philip A. Haile, 2002. "Identification of Standard Auction Models," Econometrica, Econometric Society, vol. 70(6), pages 2107-2140, November.
    13. Luo, Yao & Xiao, Ruli, 2023. "Identification of auction models using order statistics," Journal of Econometrics, Elsevier, vol. 236(1).
    14. Hu, Yingyao & McAdams, David & Shum, Matthew, 2013. "Identification of first-price auctions with non-separable unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 174(2), pages 186-193.
    15. Yingyao Hu & Geert Ridder, 2012. "Estimation of nonlinear models with mismeasured regressors using marginal information," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(3), pages 347-385, April.
    16. Simon Jäger & Benjamin Schoefer & Josef Zweimüller, 2023. "Marginal Jobs and Job Surplus: A Test of the Efficiency of Separations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(3), pages 1265-1303.
    17. Aurore Delaigle & Peter Hall, 2016. "Methodology for non-parametric deconvolution when the error distribution is unknown," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 231-252, January.
    18. Jochmans, Koen & Weidner, Martin, 2024. "Inference On A Distribution From Noisy Draws," Econometric Theory, Cambridge University Press, vol. 40(1), pages 60-97, February.
    19. An, Yonghong & Hu, Yingyao, 2012. "Well-posedness of measurement error models for self-reported data," Journal of Econometrics, Elsevier, vol. 168(2), pages 259-269.
    20. Karun Adusumilli & Taisuke Otsu, 2015. "Nonparametric instrumental regression with errors in variables," STICERD - Econometrics Paper Series /2015/585, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

    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:metrik:v:88:y:2025:i:2:d:10.1007_s00184-024-00953-5. 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.