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

2017/03/31 by Alexander Kukush, Kukush, Alexander, Oksana Chernova +1
Mathematics · #62N01 (Secondary) #62N02 (Primary) #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #msc:62N01 #msc:62N02 #stat.TH

paper · pdf · doi:10.48550/arxiv.1703.10940

arxiv created 2017/03/31 · arxiv updated 2017/04/03

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(⋅), β_n were studied for baseline hazard rate λ(⋅) and regression parameter β, at that the parameter set Θ=Θ_λ× 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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