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We consider high-dimensional inference for potentially misspecified Coxproportional hazard models based on low dimensional results by Lin and Wei[1989]. A de-sparsified Lasso estimator is proposed based on the log partiallikelihood function and shown to converge to a pseudo-true parameter vector.Interestingly, the sparsity of the true parameter can be inferred from that ofthe above limiting parameter. Moreover, each component of the above(non-sparse) estimator is shown to be asymptotically normal with a variancethat can be consistently estimated even under model misspecifications. In somecases, this asymptotic distribution leads to valid statistical inferenceprocedures, whose empirical performances are illustrated through numericalexamples.

High Dimensional Robust Inference for Cox Regression Models