2018/11/01 by Kong, Shengchun, Yu, Zhuqing, Zhang, Xianyang +1
#FOS: Mathematics #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.1811.00535
We consider high-dimensional inference for potentially misspecified Cox proportional hazard models based on low dimensional results by Lin and Wei [1989]. A de-sparsified 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 (non-sparse) 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.