Goodness-of-fit test in the Cox proportional hazards model with measurement errors

We consider the Cox proportional hazards model whose baseline hazard function $\lambda (\boldsymbol {\cdot })$ belongs to the parameter set consisting of nonnegative functions satisfying the Lipschitz condition and whose regression vector of coefficients $\beta$ belongs to a compact parameter set. The censored lifetime and corresponding values of regressors perturbed by the classical additive measurement error are observed. A goodness-of-fit test is constructed on the base of the strongly consistent simultaneous estimator of $\lambda (\boldsymbol {\cdot })$ and $\beta$ introduced in the paper by Kukush and Chernova [Teor. Imovir. Mat. Stat. 96 (2017), pp. 100-109]. The test statistic has the asymptotic chi-square distribution under the null hypothesis. The power of the test is found for corresponding local alternatives.