Confidence regions in Cox proportional hazards model with measurement errors and unbounded parameter set
Cox proportional hazards model with measurement errors is considered. In Kukush and Chernova (2017), we elaborated a simultaneous estimator of the baseline hazard rate $λ(\cdot)$ and the regression parameter $β$, with the unbounded parameter set $\varTheta=\varTheta_λ\times\varTheta_β$, where $\varTheta_λ$ is a closed convex subset of $C[0,τ]$ and $\varTheta_β$ is a compact set in $\mathbb{R}^m$. The estimator is consistent and asymptotically normal. In the present paper, we construct confidence intervals for integral functionals of $λ(\cdot)$ and a confidence region for $β$ under restrictions on the error distribution. In particular, we handle the following cases: (a) the measurement error is bounded, (b) it is a normally distributed random vector, and (c) it has independent components which are shifted Poisson random variables.