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Partially linear transformation models with varying coefficients for multivariate failure time data

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  • Qiu, Zhiping
  • Zhou, Yong

Abstract

This paper studies the estimation and inference of varying coefficients and parameters in the partially linear transformation models for multivariate failure time data. A profile martingale-based estimating method that includes global and local estimating equations is proposed. Asymptotic properties of the estimators are established. Some numerical simulations are given to show the performance of the estimation method in finite-sample situation. In order to reduce the computational burden, a simple and useful one-step estimator method is used. We further suggest a delete-a-group jackknife method to estimate asymptotic variance of estimators. A real data set from the Busselton Population Health Surveys is analyzed to illustrate the proposed methods.

Suggested Citation

  • Qiu, Zhiping & Zhou, Yong, 2015. "Partially linear transformation models with varying coefficients for multivariate failure time data," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 144-166.
    • Handle: RePEc:eee:jmvana:v:142:y:2015:i:c:p:144-166
    DOI: 10.1016/j.jmva.2015.08.008
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    References listed on IDEAS

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    1. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, November.
    2. Lu, Wenbin & Zhang, Hao Helen, 2010. "On Estimation of Partially Linear Transformation Models," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 683-691.
    3. Jane Paik Kim & Wenbin Lu & Tony Sit & Zhiliang Ying, 2013. "A Unified Approach to Semiparametric Transformation Models Under General Biased Sampling Schemes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 217-227, March.
    4. Kani Chen & Xingwei Tong, 2010. "Varying coefficient transformation models with censored data," Biometrika, Biometrika Trust, vol. 97(4), pages 969-976.
    5. Lu Tian & David Zucker & L.J. Wei, 2005. "On the Cox Model With Time-Varying Regression Coefficients," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 172-183, March.
    6. Donglin Zeng & D. Y. Lin, 2006. "Efficient estimation of semiparametric transformation models for counting processes," Biometrika, Biometrika Trust, vol. 93(3), pages 627-640, September.
    7. Kani Chen, 2002. "Semiparametric analysis of transformation models with censored data," Biometrika, Biometrika Trust, vol. 89(3), pages 659-668, August.
    8. Jianwen Cai & Jianqing Fan & Jiancheng Jiang & Haibo Zhou, 2008. "Partially linear hazard regression with varying coefficients for multivariate survival data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 141-158, February.
    9. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
    10. Cai, Jianwen & Fan, Jianqing & Jiang, Jiancheng & Zhou, Haibo, 2007. "Partially Linear Hazard Regression for Multivariate Survival Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 538-551, June.
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