We consider a model where the failure hazard function, conditional on a
covariate Z is given by R(t,θ0∣Z)=η_γ0(t)f_β0(Z),
with θ0=(β0,γ0)⊤∈Rm+p. The baseline
hazard function η_γ0 and relative risk f_β0 belong both
to parametric families. The covariate Z is measured through the error model
U=Z+ϵ where ϵ is independent from Z, with known density
f_ϵ. We observe a n-sample (X_i,D_i,U_i), i=1,...,n, where
X_i is the minimum between the failure time and the censoring time, and
D_i is the censoring indicator. We aim at estimating θ0 in presence
of the unknown density g. Our estimation procedure based on least squares
criterion provide two estimators. The first one minimizes an estimation of the
least squares criterion where g is estimated by density deconvolution. Its
rate depends on the smoothnesses of f_ϵ and f_β(z) as a
function of z,. We derive sufficient conditions that ensure the
n-consistency. The second estimator is constructed under conditions
ensuring that the least squares criterion can be directly estimated with the
parametric rate. These estimators, deeply studied through examples are in
particular n-consistent and asymptotically Gaussian in the Cox model
and in the excess risk model, whatever is f_ϵ