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Penalized spline estimation in varying coefficient models with censored data

Author

Listed:
  • K. Hendrickx

    (Hasselt University, I-BioStat)

  • P. Janssen

    (Hasselt University, I-BioStat)

  • A. Verhasselt

    (Hasselt University, I-BioStat)

Abstract

We consider P-spline smoothing in a varying coefficient regression model when the response is subject to random right censoring. We introduce two data transformation approaches to construct a synthetic response vector that is used in a penalized least squares optimization problem. We prove the consistency and asymptotic normality of the P-spline estimators for a diverging number of knots and show by simulation studies and real data examples that the combination of a data transformation for censored observations with P-spline smoothing leads to good estimators of the varying coefficient functions.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:27:y:2018:i:4:d:10.1007_s11749-017-0574-y
    DOI: 10.1007/s11749-017-0574-y
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    References listed on IDEAS

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    1. Yang, Seong Jun & El Ghouch, Anouar & Van Keilegom, Ingrid, 2014. "Varying coefficient models having different smoothing variables with randomly censored data," LIDAM Reprints ISBA 2014008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Cai, Zongwu & Fan, Jianqing & Yao, Qiwei, 2000. "Functional-coefficient regression models for nonlinear time series," LSE Research Online Documents on Economics 6314, London School of Economics and Political Science, LSE Library.
    3. Cédric Heuchenne & Ingrid Keilegom, 2007. "Polynomial Regression with Censored Data based on Preliminary Nonparametric Estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(2), pages 273-297, June.
    4. Francesco Bravo, 2014. "Varying coefficients partially linear models with randomly censored data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 383-412, April.
    5. 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.
    6. Zhezhen Jin & D. Y. Lin & Zhiliang Ying, 2006. "On least-squares regression with censored data," Biometrika, Biometrika Trust, vol. 93(1), pages 147-161, March.
    7. Sijian Wang & Bin Nan & Ji Zhu & David G. Beer, 2008. "Doubly Penalized Buckley–James Method for Survival Data with High-Dimensional Covariates," Biometrics, The International Biometric Society, vol. 64(1), pages 132-140, March.
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