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.

中文翻译：

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使用去稀疏化 Lasso 对 Cox 回归模型进行高维稳健推理

我们基于 Lin 和 Wei (1989) 的低维结果，考虑对可能错误指定的 Cox 比例风险模型进行高维推理。提出了一种基于对数偏似然函数的去稀疏化 Lasso 估计器，并显示其收敛于伪真参数向量。有趣的是，可以从上述限制参数的稀疏性推断出真实参数的稀疏性。此外，上述（非稀疏）估计量的每个分量都显示为渐近正态，具有即使在模型错误指定的情况下也可以一致估计的方差。在某些情况下，这种渐近分布会导致有效的统计推断程序，其经验性能通过数值示例进行说明。