Hypothesis testing in the Cox proportional hazards model with measurement errors

摘要

The Cox proportional hazards model with measurement errors is considered. In this model, the baseline hazard function $ lambda (oldsymbol cdot )$ belongs to a parameter set consisting of nonnegative functions satisfying the Lipschitz condition with a fixed constant, while the vector of regression coefficients $ eta $ belongs to a compact set. Censored lifetimes and corresponding regressors with additive errors are observed. Based on a simultaneous consistent estimator of the parameters of the model, $ lambda (oldsymbol cdot )$ and $ eta $, we propose a procedure of the hypothesis testing concerning the regression parameter $ eta $ and integral functional of $ lambda (oldsymbol cdot )$. The consistency of the corresponding tests is obtained.