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New M-estimators in semi-parametric regression with errors in variables

Cristina ButuceaMarie-Luce Taupin — 2008

Annales de l'I.H.P. Probabilités et statistiques

In the regression model with errors in variables, we observe i.i.d. copies of (, ) satisfying = ()+ and =+ involving independent and unobserved random variables , , plus a regression function , known up to a finite dimensional . The common densities of the ’s and of the ’s are unknown, whereas the distribution of is completely known. We aim at estimating the parameter by using the observations ( ...

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

Marie-Laure Martin-MagnietteMarie-Luce Taupin — 2009

ESAIM: Probability and Statistics

We consider a failure hazard function, conditional on a time-independent covariate , given by η γ 0 ( t ) f β 0 ( Z ) . The baseline hazard function η γ 0 and the relative risk f β 0 both belong to parametric families with θ 0 = ( β 0 , γ 0 ) m + p . 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 f ε . We observe a -sample , = 1, ..., , where is the minimum between the failure time and the censoring time, and ...

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