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
Document type :
Journal articles
Complete list of metadatas

Cited literature [38 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00480192
Contributor : Hal Peer <>
Submitted on : Monday, May 3, 2010 - 3:53:50 PM
Last modification on : Saturday, February 8, 2020 - 2:39:44 PM
Long-term archiving on: Thursday, December 1, 2016 - 12:09:20 AM

File

PEER_stage2_10.1051%2Fps%3A200...
Files produced by the author(s)

Identifiers

Citation

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⟩

Share

Metrics

Record views

238

Files downloads

202