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arXiv · 1703.10940

Consistent estimation in Cox proportional hazards model with measurement errors and unbounded parameter set

Alexander Kukush·Oksana Chernova
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Abstract

Cox proportional hazards model with measurement error is investigated. In Kukush et al. (2011) [Journal of Statistical Research 45, 77-94] and Chimisov and Kukush (2014) [Modern Stochastics: Theory and Applications 1, 13-32] asymptotic properties of simultaneous estimator $λ_n(\cdot)$, $β_n$ were studied for baseline hazard rate $λ(\cdot)$ and regression parameter $β$, at that the parameter set $Θ=Θ_λ\times Θ_β$ was assumed bounded. In the present paper, the set $Θ_λ$ is unbounded from above and 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.

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Alexander Kukush, Oksana Chernova. 2017-03-31. Consistent estimation in Cox proportional hazards model with measurement errors and unbounded parameter set. https://arxiv.org/abs/1703.10940

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