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Partial marginal likelihood estimation for general transformation models

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  • Gu, Minggao
  • Wu, Yueqin
  • Huang, Bin

Abstract

We consider a large class of transformation models introduced by Gu et al. (2005) [14]. They proposed an estimation procedure for calculating the maximum partial marginal likelihood estimator (MPMLE) of regression parameters. A big advantage of MPMLE is that it avoids estimating two infinitely dimensional nuisance parameters: baseline and censoring survival functions. And they showed the validity of MPMLE through extensive simulations. In this paper, we establish the asymptotic properties of MPMLE in the general transformation models for either right or left censored data. The difficulty in establishing these asymptotic results comes from the fact that the score function derived from the partial marginal likelihood does not have ordinary independence or martingale structure. We develop a novel discretization method to resolve the difficulty. The estimation procedure is further examined using simulation studies and the analysis of the ACTG019 data.

Suggested Citation

  • Gu, Minggao & Wu, Yueqin & Huang, Bin, 2014. "Partial marginal likelihood estimation for general transformation models," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 1-18.
    • Handle: RePEc:eee:jmvana:v:123:y:2014:i:c:p:1-18
    DOI: 10.1016/j.jmva.2013.08.016
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    References listed on IDEAS

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    1. Wenbin Lu & Anastasios A. Tsiatis, 2006. "Semiparametric transformation models for the case-cohort study," Biometrika, Biometrika Trust, vol. 93(1), pages 207-214, March.
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    3. Wenbin Lu, 2004. "On semiparametric transformation cure models," Biometrika, Biometrika Trust, vol. 91(2), pages 331-343, June.
    4. Kelly Zou & W. J. Hall, 2000. "Two transformation models for estimating an ROC curve derived from continuous data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(5), pages 621-631.
    5. Ming Gao Gu & Hong‐Tu Zhu, 2001. "Maximum likelihood estimation for spatial models by Markov chain Monte Carlo stochastic approximation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 339-355.
    6. Guozhi Gao & Anastasios A. Tsiatis, 2005. "Semiparametric estimators for the regression coefficients in the linear transformation competing risks model with missing cause of failure," Biometrika, Biometrika Trust, vol. 92(4), pages 875-891, December.
    7. 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.
    8. Kani Chen, 2002. "Semiparametric analysis of transformation models with censored data," Biometrika, Biometrika Trust, vol. 89(3), pages 659-668, August.
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