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On sparse estimation for semiparametric linear transformation models


  • Zhang, Hao Helen
  • Lu, Wenbin
  • Wang, Hansheng


Semiparametric linear transformation models have received much attention due to their high flexibility in modeling survival data. A useful estimating equation procedure was recently proposed by Chen et al. (2002) [21] for linear transformation models to jointly estimate parametric and nonparametric terms. They showed that this procedure can yield a consistent and robust estimator. However, the problem of variable selection for linear transformation models has been less studied, partially because a convenient loss function is not readily available under this context. In this paper, we propose a simple yet powerful approach to achieve both sparse and consistent estimation for linear transformation models. The main idea is to derive a profiled score from the estimating equation of Chen et al. [21], construct a loss function based on the profile scored and its variance, and then minimize the loss subject to some shrinkage penalty. Under regularity conditions, we have shown that the resulting estimator is consistent for both model estimation and variable selection. Furthermore, the estimated parametric terms are asymptotically normal and can achieve a higher efficiency than that yielded from the estimation equations. For computation, we suggest a one-step approximation algorithm which can take advantage of the LARS and build the entire solution path efficiently. Performance of the new procedure is illustrated through numerous simulations and real examples including one microarray data.

Suggested Citation

  • Zhang, Hao Helen & Lu, Wenbin & Wang, Hansheng, 2010. "On sparse estimation for semiparametric linear transformation models," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1594-1606, August.
  • Handle: RePEc:eee:jmvana:v:101:y:2010:i:7:p:1594-1606

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    References listed on IDEAS

    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Hui Zou, 2008. "A note on path-based variable selection in the penalized proportional hazards model," Biometrika, Biometrika Trust, vol. 95(1), pages 241-247.
    3. Johnson, Brent A. & Lin, D.Y. & Zeng, Donglin, 2008. "Penalized Estimating Functions and Variable Selection in Semiparametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 672-680, June.
    4. Wang, Hansheng & Li, Guodong & Jiang, Guohua, 2007. "Robust Regression Shrinkage and Consistent Variable Selection Through the LAD-Lasso," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 347-355, July.
    5. Hansheng Wang & Guodong Li & Chih‐Ling Tsai, 2007. "Regression coefficient and autoregressive order shrinkage and selection via the lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(1), pages 63-78, February.
    6. Zeng, Donglin & Lin, D.Y., 2007. "Semiparametric Transformation Models With Random Effects for Recurrent Events," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 167-180, March.
    7. Wang, Hansheng & Leng, Chenlei, 2007. "Unified LASSO Estimation by Least Squares Approximation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1039-1048, 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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    Cited by:

    1. Hu, Jianwei & Chai, Hao, 2013. "Adjusted regularized estimation in the accelerated failure time model with high dimensional covariates," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 96-114.
    2. repec:spr:stpapr:v:58:y:2017:i:3:d:10.1007_s00362-015-0721-z is not listed on IDEAS
    3. Li, Jianbo & Gu, Minggao & Zhang, Riquan, 2013. "Variable selection for general transformation models with right censored data via nonconcave penalties," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 445-456.
    4. Zhangong Zhou & Rong Jiang & Weimin Qian, 2013. "LAD variable selection for linear models with randomly censored data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(2), pages 287-300, February.
    5. Li, Jianbo & Gu, Minggao, 2012. "Adaptive LASSO for general transformation models with right censored data," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2583-2597.


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