Modern Stochastics: Theory and Applications

Cox proportional hazards model is considered. In Kukush et al. (2011), Journal of Statistical Research, Vol. 45, No. 2, 77–94 simultaneous estimators $\lambda _{n}(\cdot )$ and $\beta _{n}$ of baseline hazard rate $\lambda (\cdot )$ and regression parameter β are studied. The estimators maximize the objective function that corrects the log-likelihood function for measurement errors and censoring. Parameter sets for $\lambda (\cdot )$ and β are convex compact sets in $C[0,\tau ]$ and ${\mathbb{R}}^{k}$, respectively. In present paper the asymptotic normality for $\beta _{n}$ and linear functionals of $\lambda _{n}(\cdot )$ is shown. The results are valid as well for a model without measurement errors. A way to compute the estimators is discussed based on the fact that $\lambda _{n}(\cdot )$ is a linear spline.