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Adaptive Lasso for Cox’s proportional hazards model. (English) Zbl 1135.62083
Summary: We investigate the variable selection problem for Cox’s proportional hazards model, and propose a unified model selection and estimation procedure with desired theoretical properties and computational convenience. The new method is based on a penalized log partial likelihood with the adaptively weighted $$L_1$$ penalty on regression coefficients, providing what we call the adaptive Lasso estimator. The method incorporates different penalties for different coefficients: unimportant variables receive larger penalties than important ones, so that important variables tend to be retained in the selection process, whereas unimportant variables are more likely to be dropped.
Theoretical properties, such as consistency and rate of convergence of the estimator, are studied. We also show that, with proper choice of regularization parameters, the proposed estimator has the oracle properties. The convex optimization nature of the method leads to an efficient algorithm. Both simulated and real examples show that the method performs competitively.

##### MSC:
 62N02 Estimation in survival analysis and censored data 62G20 Asymptotic properties of nonparametric inference 65C60 Computational problems in statistics (MSC2010)
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