Abstract
Project Number
Not Applicable
References
- [1] R. Beran, Nonparametric regression with randomly censored data, Technical Report, University of California, Berkeley, 1981.
- [2] J. Buckley and I. James, Linear regression with censored data, Biometrika 66(3), 429–436, 1979.
- [3] A. Chaudhuri and H. Loh, Nonparametric regression under right censoring: A modern review, Statist. Surv. 14, 1–38, 2020.
- [4] S.X. Chen and M. Zhou, Nonparametric regression with censored survival data, Scand. J. Stat. 14(4), 181–197, 1987.
- [5] S.X. Chen and M. Zhou, Local polynomial regression analysis of censored data, J. Multivar. Anal. 98(4), 1005–1027, 2007.
- [6] D. Dabrowska, Estimation of survival functions under dependent censoring, Scand. J. Stat. 32, 265–280, 2005.
- [7] M. Einmahl, I. Van Keilegom, and D. Zhou, Regression analysis with censored data: recent developments, J. Multivar. Anal. 176, 104581, 2020.
- [8] J. Fan and I. Gijbels, Local Polynomial Modelling and Its Applications, Chapman & Hall, London, 1994.
- [9] J. Fan and Y.K. Truong, Nonparametric regression with errors in variables, Ann. Stat. 21(4), 1900–1925, 1993.
- [10] I. Gijbels, R.J. Hyndman, and N. Veraverbeke, Nonparametric hazard estimation under random censoring with boundary correction, Chapman & Hall/CRC, 1999.
- [11] I. Gijbels and L. Peng, Estimation of a smooth monotone hazard function, Scand. J. Stat. 27(3), 411–427, 2000.
- [12] W. González-Manteiga and M.D. Martínez-Miranda, Kernel estimation of a regression function with dependent censoring, Comput. Stat. Data Anal. 50(2), 540–553, 2006.
- [13] Y. He and J. Huang, Transformation-based nonparametric regression with censored responses, Comput. Stat. Data Anal. 164, 107307, 2022.
- [14] M.C. Jones, J.S. Marron, and S.J. Sheather, A brief survey of bandwidth selection for density estimation, J. Am. Stat. Assoc. 91(433), 401–407, 1996.
- [15] E.L. Kaplan and P. Meier, Nonparametric estimation from incomplete observations, J. Am. Stat. Assoc. 53(282), 457–481, 1958.
- [16] H.L. Koul, V. Susarla, and J. Van Ryzin, Regression estimation with randomly rightcensored data, Ann. Stat. 9(3), 1276–1288, 1981.
- [17] O. Lopez and V. Patilea, Uniform convergence rates for kernel estimators with dependent censoring, Electron. J. Stat. 11(1), 292–325, 2017.
- [18] L. Lopez and I. Van Keilegom, Robust nonparametric regression for censored data, TEST 31, 925–954, 2022.
- [19] W. Lu and A.A. Tsiatis, Nonparametric estimation of marginal regression functions with censored data, J. Am. Stat. Assoc. 96(456), 1031–1042, 2001.
- [20] J. Mielniczuk and A. Wojewódka, Nonparametric regression estimation for rightcensored data, J. Nonparametr. Stat. 28(4), 591–606, 2016.
- [21] E.A. Nadaraya, On estimating regression, Theory Probab. Appl. 9, 141–142, 1964.
- [22] S. Qin and Z. Zhang, Kernel-based IPCW estimation for censored regression models, J. Nonparametr. Stat. 35(2), 245–270, 2023.
- [23] J. Rice and B.W. Silverman, Estimating the mean and covariance structure nonparametrically when the data are curves, J. R. Stat. Soc. Ser. B 53(1), 233–243, 1991.
- [24] W. Stute, Consistent estimation under random censorship when covariables are present, J. Multivar. Anal. 45(1), 89–103, 1993.
- [25] W. Stute and R. Song, A model check for regression under random censorship, Stat. Probab. Lett. 17(5), 315–321, 1993.
- [26] T.M. Therneau, A Package for Survival Analysis in R, R package version 3.5-7, 2023.
- [27] Y. Wang and N. Wang, A kernel regression estimator for censored data under random censoring, Scand. J. Stat. 38(1), 41–58, 2011.
- [28] Y. Wang, M. Zhou, and X. Li, Conditional inverse probability weighting for nonparametric regression under censoring, Scand. J. Stat. 51(1), 2024.
- [29] X. Zhou and P.S.F. Yip, Nonparametric estimation of a regression function with censored data using local polynomial fitting, Biometrika 86(1), 103–113, 1999.
A transformation-based conditional IPCW kernel estimator for nonparametric regression under right censoring
Abstract
In survival analysis and reliability studies, right-censored data frequently arise, which poses significant challenges in accurately estimating regression functions. This paper proposes a transformation-based conditional inverse probability of censoring weighted kernel estimator for the regression function in the presence of right censoring. Traditional kernel-based regression techniques often fail to properly account for censoring, resulting in biased estimates. To address this issue, the proposed estimator combines a monotonic transformation of the response variable with a conditional inverse probability of censoring weighted approach. The transformation reduces variability and enhances finite-sample performance, while the conditional inverse probability of weighted censoring adjusts for the censoring mechanism through kernel smoothing in the covariate space. The asymptotic properties of the estimator, including consistency and asymptotic normality, are established. Simulation studies demonstrate improved bias reduction and competitive mean squared error performance compared to classical approaches, such as the naive, substitution, and marginal inverse probability of censoring weighted estimators, especially under moderate to heavy censoring. An application to the primary biliary cirrhosis dataset further illustrates the advantages of the proposed estimator in a real-world medical setting.
Keywords
Asymptotic theory inverse probability weighting kernel smoothing nonparametric regression right censoring transformation
Ethical Statement
This study does not involve any experiments on humans or animals. The data used are publicly available, and no ethical approval was required
Supporting Institution
Ministry of Higher Education and Scientific Research (Algeria) and University of Biskra
Project Number
Not Applicable
Thanks
The author would like to express their sincere gratitude to the Ministry of Higher Education and Scientific Research (Algeria) for its financial and institutional support. The author also thank the anonymous reviewers for their valuable comments and suggestions that improved the quality of this manuscript
References
- [1] R. Beran, Nonparametric regression with randomly censored data, Technical Report, University of California, Berkeley, 1981.
- [2] J. Buckley and I. James, Linear regression with censored data, Biometrika 66(3), 429–436, 1979.
- [3] A. Chaudhuri and H. Loh, Nonparametric regression under right censoring: A modern review, Statist. Surv. 14, 1–38, 2020.
- [4] S.X. Chen and M. Zhou, Nonparametric regression with censored survival data, Scand. J. Stat. 14(4), 181–197, 1987.
- [5] S.X. Chen and M. Zhou, Local polynomial regression analysis of censored data, J. Multivar. Anal. 98(4), 1005–1027, 2007.
- [6] D. Dabrowska, Estimation of survival functions under dependent censoring, Scand. J. Stat. 32, 265–280, 2005.
- [7] M. Einmahl, I. Van Keilegom, and D. Zhou, Regression analysis with censored data: recent developments, J. Multivar. Anal. 176, 104581, 2020.
- [8] J. Fan and I. Gijbels, Local Polynomial Modelling and Its Applications, Chapman & Hall, London, 1994.
- [9] J. Fan and Y.K. Truong, Nonparametric regression with errors in variables, Ann. Stat. 21(4), 1900–1925, 1993.
- [10] I. Gijbels, R.J. Hyndman, and N. Veraverbeke, Nonparametric hazard estimation under random censoring with boundary correction, Chapman & Hall/CRC, 1999.
- [11] I. Gijbels and L. Peng, Estimation of a smooth monotone hazard function, Scand. J. Stat. 27(3), 411–427, 2000.
- [12] W. González-Manteiga and M.D. Martínez-Miranda, Kernel estimation of a regression function with dependent censoring, Comput. Stat. Data Anal. 50(2), 540–553, 2006.
- [13] Y. He and J. Huang, Transformation-based nonparametric regression with censored responses, Comput. Stat. Data Anal. 164, 107307, 2022.
- [14] M.C. Jones, J.S. Marron, and S.J. Sheather, A brief survey of bandwidth selection for density estimation, J. Am. Stat. Assoc. 91(433), 401–407, 1996.
- [15] E.L. Kaplan and P. Meier, Nonparametric estimation from incomplete observations, J. Am. Stat. Assoc. 53(282), 457–481, 1958.
- [16] H.L. Koul, V. Susarla, and J. Van Ryzin, Regression estimation with randomly rightcensored data, Ann. Stat. 9(3), 1276–1288, 1981.
- [17] O. Lopez and V. Patilea, Uniform convergence rates for kernel estimators with dependent censoring, Electron. J. Stat. 11(1), 292–325, 2017.
- [18] L. Lopez and I. Van Keilegom, Robust nonparametric regression for censored data, TEST 31, 925–954, 2022.
- [19] W. Lu and A.A. Tsiatis, Nonparametric estimation of marginal regression functions with censored data, J. Am. Stat. Assoc. 96(456), 1031–1042, 2001.
- [20] J. Mielniczuk and A. Wojewódka, Nonparametric regression estimation for rightcensored data, J. Nonparametr. Stat. 28(4), 591–606, 2016.
- [21] E.A. Nadaraya, On estimating regression, Theory Probab. Appl. 9, 141–142, 1964.
- [22] S. Qin and Z. Zhang, Kernel-based IPCW estimation for censored regression models, J. Nonparametr. Stat. 35(2), 245–270, 2023.
- [23] J. Rice and B.W. Silverman, Estimating the mean and covariance structure nonparametrically when the data are curves, J. R. Stat. Soc. Ser. B 53(1), 233–243, 1991.
- [24] W. Stute, Consistent estimation under random censorship when covariables are present, J. Multivar. Anal. 45(1), 89–103, 1993.
- [25] W. Stute and R. Song, A model check for regression under random censorship, Stat. Probab. Lett. 17(5), 315–321, 1993.
- [26] T.M. Therneau, A Package for Survival Analysis in R, R package version 3.5-7, 2023.
- [27] Y. Wang and N. Wang, A kernel regression estimator for censored data under random censoring, Scand. J. Stat. 38(1), 41–58, 2011.
- [28] Y. Wang, M. Zhou, and X. Li, Conditional inverse probability weighting for nonparametric regression under censoring, Scand. J. Stat. 51(1), 2024.
- [29] X. Zhou and P.S.F. Yip, Nonparametric estimation of a regression function with censored data using local polynomial fitting, Biometrika 86(1), 103–113, 1999.
Details
| Primary Language | English |
|---|---|
| Subjects | Applied Statistics |
| Journal Section | Research Article |
| Authors | |
| Project Number | Not Applicable |
| Submission Date | August 13, 2025 |
| Acceptance Date | January 4, 2026 |
| Early Pub Date | February 2, 2026 |
| Publication Date | February 2, 2026 |
| DOI | https://doi.org/10.15672/hujms.1763672 |
| IZ | https://izlik.org/JA54AE55YH |
| Published in Issue | Year 2026 Volume: 55 Issue: 1 |
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