Cai Jianwen, Fan Jianqing, Li Runze, Zhou Haibo
Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-7420, U.S.A.,
Biometrika. 2005;92(2):303-316. doi: 10.1093/biomet/92.2.303.
In this paper, we proposed a penalised pseudo-partial likelihood method for variable selection with multivariate failure time data with a growing number of regression coefficients. Under certain regularity conditions, we show the consistency and asymptotic normality of the penalised likelihood estimators. We further demonstrate that, for certain penalty functions with proper choices of regularisation parameters, the resulting estimator can correctly identify the true model, as if it were known in advance. Based on a simple approximation of the penalty function, the proposed method can be easily carried out with the Newton-Raphson algorithm. We conduct extensive Monte Carlo simulation studies to assess the finite sample performance of the proposed procedures. We illustrate the proposed method by analysing a dataset from the Framingham Heart Study.
在本文中，我们提出了一种惩罚伪偏似然方法，用于对具有不断增加的回归系数的多变量失效时间数据进行变量选择。在某些正则性条件下，我们证明了惩罚似然估计量的一致性和渐近正态性。我们进一步证明，对于某些惩罚函数，通过适当选择正则化参数，所得估计量能够正确识别真实模型，就好像它是事先已知的一样。基于惩罚函数的一个简单近似，所提出的方法可以很容易地通过牛顿-拉夫森算法来实现。我们进行了广泛的蒙特卡罗模拟研究，以评估所提出方法的有限样本性能。我们通过分析来自弗雷明汉心脏研究的一个数据集来说明所提出的方法。
