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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
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    References listed on IDEAS

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    1. 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).
    2. 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.
    3. 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.
    4. 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.
    5. 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.
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