High-dimensional robust inference for Cox regression models using desparsified Lasso
High-dimensional robust inference for Cox regression models using desparsified Lasso
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DOI：
10.1111/sjos.12543
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发表时间：
2021-07-19
影响因子：
1
通讯作者：
Cheng, Guang
中科院分区：
文献类型：
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作者：
Kong, Shengchun;Yu, Zhuqing;Cheng, Guang
我们考虑基于Lin和Wei（1989）的低维结果对可能错误指定的Cox比例风险模型进行高维推断。提出了一种基于对数偏似然函数的非稀疏Lasso估计，并证明了该估计收敛于伪真参数向量。有趣的是，真参数的稀疏性可以从上述极限参数的稀疏性推断出来。此外，上述（非稀疏）估计量的每个分量都被证明是渐近正态的，其方差即使在模型错误规范下也可以被一致地估计。在某些情况下，这种渐近分布导致有效的统计推断程序，其经验性能通过数值例子说明。
We consider high-dimensional inference for potentially misspecified Cox proportional hazard models based on low-dimensional results by Lin and Wei (1989). A desparsified Lasso estimator is proposed based on the log partial likelihood function and shown to converge to a pseudo-true parameter vector. Interestingly, the sparsity of the true parameter can be inferred from that of the above limiting parameter. Moreover, each component of the above (nonsparse) estimator is shown to be asymptotically normal with a variance that can be consistently estimated even under model misspecifications. In some cases, this asymptotic distribution leads to valid statistical inference procedures, whose empirical performances are illustrated through numerical examples.