Asymptotic normality of corrected estimator in Cox proportional hazards model with measurement error

Abstract

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.

Keywords

• Asymptotic normality of estimators
• classical measurement error
• Corrected Maximum Likelihood Estimator
• Cox proportional hazards model
• estimator of baseline hazards function