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Prediction from Randomly Right Censored Data

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  • Kohler, Michael
  • Máthé, Kinga
  • Pintér, Márta

Abstract

Let X be a random vector taking values in d, let Y be a bounded random variable, and let C be a right censoring random variable operating on Y. It is assumed that C is independent of (X, Y), the distribution function of C is continuous, and the support of the distribution of Y is a proper subset of the support of the distribution of C. Given a sample {Xi, min{Yi, Ci}, I[Yi[less-than-or-equals, slant]Ci]} and a vector of covariates X, we want to construct an estimate of Y such that the mean squared error is minimized. Without censoring, i.e., for C=[infinity] almost surely, it is well known that the mean squared error of suitably defined kernel, partitioning, nearest neighbor, least squares, and smoothing spline estimates converges for every distribution of (X, Y) to the optimal value almost surely, if the sample size tends to infinity. In this paper, we modify the above estimates and show that in the random right censoring model described above the same is true for the modified estimates.

Suggested Citation

  • Kohler, Michael & Máthé, Kinga & Pintér, Márta, 2002. "Prediction from Randomly Right Censored Data," Journal of Multivariate Analysis, Elsevier, vol. 80(1), pages 73-100, January.
  • Handle: RePEc:eee:jmvana:v:80:y:2002:i:1:p:73-100
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    References listed on IDEAS

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    Cited by:

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    2. Ersin Yılmaz & Syed Ejaz Ahmed & Dursun Aydın, 2020. "A-Spline Regression for Fitting a Nonparametric Regression Function with Censored Data," Stats, MDPI, vol. 3(2), pages 1-17, May.
    3. Bouzebda, Salim & Chaouch, Mohamed, 2022. "Uniform limit theorems for a class of conditional Z-estimators when covariates are functions," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    4. Messaci, Fatiha, 2010. "Local averaging estimates of the regression function with twice censored data," Statistics & Probability Letters, Elsevier, vol. 80(19-20), pages 1508-1511, October.
    5. Liang, Han-Ying & Li, Deli & Qi, Yongcheng, 2009. "Strong convergence in nonparametric regression with truncated dependent data," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 162-174, January.
    6. Salim Bouzebda & Amel Nezzal & Tarek Zari, 2022. "Uniform Consistency for Functional Conditional U -Statistics Using Delta-Sequences," Mathematics, MDPI, vol. 11(1), pages 1-39, December.
    7. Kebabi, K. & Laroussi, I. & Messaci, F., 2011. "Least squares estimators of the regression function with twice censored data," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1588-1593, November.
    8. Saâdia Rahmani & Oussama Bouanani, 2023. "Local linear estimation of the conditional cumulative distribution function: Censored functional data case," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 741-769, February.
    9. Salah, Khardani & Yousri, Slaoui, 2019. "Nonparametric relative regression under random censorship model," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 116-122.
    10. Salim Bouzebda & Thouria El-hadjali & Anouar Abdeldjaoued Ferfache, 2023. "Uniform in Bandwidth Consistency of Conditional U-statistics Adaptive to Intrinsic Dimension in Presence of Censored Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1548-1606, August.
    11. Mohamed Lemdani & Elias Ould Saïd, 2017. "Nonparametric robust regression estimation for censored data," Statistical Papers, Springer, vol. 58(2), pages 505-525, June.
    12. Debbarh, Mohammed & Viallon, Vivian, 2008. "Testing additivity in nonparametric regression under random censorship," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2584-2591, November.

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