Estimation of the hazard function in a semiparametric model with covariate measurement error

Abstract : We consider a failure hazard function, conditional on a time-independent covariate , given by . The baseline hazard function and the relative risk both belong to parametric families with . The covariate has an unknown density and is measured with an error through an additive error model where is a random variable, independent from , with known density . We observe a -sample , = 1, ..., , where is the minimum between the failure time and the censoring time, and is the censoring indicator. Using least square criterion and deconvolution methods, we propose a consistent estimator of using the observations , = 1, ..., .
We give an upper bound for its risk which depends on the smoothness properties of and as a function of , and we derive sufficient conditions for the -consistency. We give detailed examples considering various type of relative risks and various types of error density . In particular, in the Cox model and in the excess risk model, the estimator of is -consistent and asymptotically Gaussian regardless of the form of .
Keywords : Mathematics
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Article dans une revue
ESAIM: Probability and Statistics, EDP Sciences, 2009, 13, pp.87-114. <10.1051/ps:2008004>
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Soumis le : lundi 3 mai 2010 - 15:53:50
Dernière modification le : samedi 18 février 2017 - 01:19:43
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Marie-Laure Martin-Magniette, Marie-Luce Taupin. Estimation of the hazard function in a semiparametric model with covariate measurement error. ESAIM: Probability and Statistics, EDP Sciences, 2009, 13, pp.87-114. <10.1051/ps:2008004>. <hal-00480192>

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