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Theory of Probability and Mathematical Statistics



CONSISTENT ESTIMATION IN COX PROPORTIONAL HAZARDS MODEL WITH MEASUREMENT ERRORS AND UNBOUNDED PARAMETER SET

A. G. KUKUSH, O. O. CHERNOVA

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Abstract: Cox proportional hazards model with measurement error is investigated. In \cite{KuBar} and \cite{ChiKu} asymptotic properties were studied of simultaneous estimator $\lambda_n(\cdot)$, $\beta_n$ for baseline hazard rate $\lambda(\cdot)$ and regression parameter $\beta$, at that the parameter set $\Theta=\Theta_{\lambda}\times \Theta_{\beta}$ was assumed bounded. In the present paper, the set $\Theta_{\lambda}$ is unbounded from above and is not separated away from $0$. We construct the estimator in two steps: first we derive a strongly consistent estimator and then modify it to provide its asymptotic normality.

Keywords: Асимптотично нормальна оцінка, консистентна оцінка, модель Кокса з пропорційними ризиками, сумісне оцінювання базової функції ризику та параметра регресії

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