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Non‐parametric Regression with Dependent Censored Data

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  • ANOUAR EL GHOUCH
  • INGRID VAN KEILEGOM

Abstract

. Let (Xi,Yi) (i=1,…,n) be n replications of a random vector (X,Y ), where Y is supposed to be subject to random right censoring. The data (Xi,Yi) are assumed to come from a stationary α‐mixing process. We consider the problem of estimating the function m(x) =ℰ(φ(Y) | X=x), for some known transformation φ. This problem is approached in the following way: first, we introduce a transformed variable , that is not subject to censoring and satisfies the relation , and then we estimate m(x) by applying local linear regression techniques. As a by‐product, we obtain a general result on the uniform rate of convergence of kernel type estimators of functionals of an unknown distribution function, under strong mixing assumptions.

Suggested Citation

  • Anouar El Ghouch & Ingrid Van Keilegom, 2008. "Non‐parametric Regression with Dependent Censored Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(2), pages 228-247, June.
    • Handle: RePEc:bla:scjsta:v:35:y:2008:i:2:p:228-247
    DOI: 10.1111/j.1467-9469.2007.00586.x
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    Cited by:

    1. Bordes, Laurent & Gneyou, Kossi Essona, 2011. "Uniform convergence of nonparametric regressions in competing risk models with right censoring," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1654-1663, November.
    2. K. Hendrickx & P. Janssen & A. Verhasselt, 2018. "Penalized spline estimation in varying coefficient models with censored data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(4), pages 871-895, December.
    3. 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.
    4. Han-Ying Liang & Jacobo Uña-álvarez & María Iglesias-pérez, 2015. "A Central Limit Theorem in Non-parametric Regression with Truncated, Censored and Dependent Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 256-269, March.
    5. Han-Ying Liang, 2012. "Weighted nonparametric regression estimation with truncated and dependent data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 1051-1073, December.
    6. Talamakrouni, Majda & El Ghouch, Anouar & Van Keilegom, Ingrid, 2016. "Parametrically guided local quasi-likelihood with censored data," LIDAM Discussion Papers ISBA 2016011, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. 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).
    8. Han-Ying Liang & Jacobo Uña-Álvarez & María Iglesias-Pérez, 2011. "Local polynomial estimation of a conditional mean function with dependent truncated data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 653-677, November.
    9. Bouhadjera Feriel & Saïd Elias Ould, 2021. "Asymptotic normality of the relative error regression function estimator for censored and time series data," Dependence Modeling, De Gruyter, vol. 9(1), pages 156-178, January.

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