Confidence regions in Cox proportional hazards model with measurement errors and unbounded parameter set

Modern Stochastics: Theory and Applications

卷:5

Alexander Kukush¹  Oksana Chernova¹ 

[1] Taras Shevchenko National University of Kyiv, Kyiv, Ukraine;

关键词: Asymptotic normality;    confidence region;    consistent estimator;    Cox proportional hazards model;    measurement errors;    simultaneous estimation of baseline hazard rate and regression parameter;   

DOI  :  10.15559/18-VMSTA94

来源: DOAJ

【 摘 要 】

Cox proportional hazards model with measurement errors is considered. In Kukush and Chernova (2017), we elaborated a simultaneous estimator of the baseline hazard rate $\lambda (\cdot )$ and the regression parameter β, with the unbounded parameter set $\varTheta =\varTheta _{\lambda }\times \varTheta _{\beta }$, where $\varTheta _{\lambda }$ is a closed convex subset of $C[0,\tau ]$ and $\varTheta _{\beta }$ 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 $\lambda (\cdot )$ 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.

【 授权许可】

Unknown