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Partially varying coefficient single index proportional hazards regression models

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  • Li, Jianbo
  • Zhang, Riquan

Abstract

In this paper, the partially varying coefficient single index proportional hazards regression models are discussed. All unknown functions are fitted by polynomial B splines. The index parameters and B-spline coefficients are estimated by the partial likelihood method and a two-step Newton-Raphson algorithm. Consistency and asymptotic normality of the estimators of all the parameters are derived. Through a simulation study and the VA data example, we illustrate that the proposed estimation procedure is accurate, rapid and stable.

Suggested Citation

  • Li, Jianbo & Zhang, Riquan, 2011. "Partially varying coefficient single index proportional hazards regression models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 389-400, January.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:389-400
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    References listed on IDEAS

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    1. Nielsen, Jens P. & Linton, Oliver & Bickel, Peter J., 1998. "On a semiparametric survival model with flexible covariate effect," LSE Research Online Documents on Economics 301, London School of Economics and Political Science, LSE Library.
    2. Peter D. Sasieni, 2003. "Martingale difference residuals as a diagnostic tool for the Cox model," Biometrika, Biometrika Trust, vol. 90(4), pages 899-912, December.
    3. Murphy, S. A. & Sen, P. K., 1991. "Time-dependent coefficients in a Cox-type regression model," Stochastic Processes and their Applications, Elsevier, vol. 39(1), pages 153-180, October.
    4. Jianhua Z. Huang & Linxu Liu, 2006. "Polynomial Spline Estimation and Inference of Proportional Hazards Regression Models with Flexible Relative Risk Form," Biometrics, The International Biometric Society, vol. 62(3), pages 793-802, September.
    5. Gørgens, Tue, 2004. "Average Derivatives For Hazard Functions," Econometric Theory, Cambridge University Press, vol. 20(3), pages 437-463, June.
    6. Sun, Jie & Kopciuk, Karen A. & Lu, Xuewen, 2008. "Polynomial spline estimation of partially linear single-index proportional hazards regression models," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 176-188, September.
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    Cited by:

    1. Zhensheng Huang & Xing Sun & Riquan Zhang, 2022. "Estimation for partially varying-coefficient single-index models with distorted measurement errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(2), pages 175-201, February.
    2. Qingming Zou & Zhongyi Zhu, 2014. "M-estimators for single-index model using B-spline," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(2), pages 225-246, February.
    3. Lin Liu & Jianbo Li & Riquan Zhang, 2014. "General partially linear additive transformation model with right-censored data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(10), pages 2257-2269, October.
    4. Jianbo Li & Minggao Gu & Tao Hu, 2012. "General partially linear varying-coefficient transformation models for ranking data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(7), pages 1475-1488, January.
    5. Shang, Shulian & Liu, Mengling & Zeleniuch-Jacquotte, Anne & Clendenen, Tess V. & Krogh, Vittorio & Hallmans, Goran & Lu, Wenbin, 2013. "Partially linear single index Cox regression model in nested case-control studies," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 199-212.

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