Variable selection in Cox regression models with varying coefficients
We deal with two kinds of Cox regression models with varying coefficients. The coefficients vary with time in one model. In the other model, there is an important random variable called an index variable and the coefficients vary with the variable. In both models, we have p-dimensional covariates and p increases moderately. However, it is the case that only a small part of the covariates are relevant in these situations. We carry out variable selection and estimation of the coefficient functions by using the group SCAD-type estimator and the adaptive group Lasso estimator. We examine the theoretical properties of the estimators, especially the L2 convergence rate, the sparsity, and the oracle property. Simulation studies and a real data analysis show the performance of these new techniques.
|Date of creation:||Oct 2012|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: http://sfb649.wiwi.hu-berlin.de
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Lukas Meier & Sara van de Geer & Peter Bühlmann, 2008. "The group lasso for logistic regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 53-71.
- 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.
- S. Wang & B. Nan & N. Zhu & J. Zhu, 2009. "Hierarchically penalized Cox regression with grouped variables," Biometrika, Biometrika Trust, vol. 96(2), pages 307-322.
- Zhang, Hao Helen & Cheng, Guang & Liu, Yufeng, 2011. "Linear or Nonlinear? Automatic Structure Discovery for Partially Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1099-1112.
- 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.
- Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67.
- Jianwen Cai & Jianqing Fan & Runze Li & Haibo Zhou, 2005. "Variable selection for multivariate failure time data," Biometrika, Biometrika Trust, vol. 92(2), pages 303-316, June.
- Hao Helen Zhang & Wenbin Lu, 2007. "Adaptive Lasso for Cox's proportional hazards model," Biometrika, Biometrika Trust, vol. 94(3), pages 691-703.
- Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
When requesting a correction, please mention this item's handle: RePEc:hum:wpaper:sfb649dp2012-061. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (RDC-Team)
If references are entirely missing, you can add them using this form.