Semi-parametric estimation of the hazard function in a model with covariate measurement error

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dc.creatorMartin-Magniette, Marie-Laure
dc.creatorTaupin, Marie-Luce
dc.date2006-06-08
dc.date.accessioned2026-07-07T08:07:54Z
dc.date.available2026-07-07T08:07:54Z
dc.descriptionWe consider a model where the failure hazard function, conditional on a covariate $Z$ is given by $R(t,θ^0|Z)=η\_{γ^0}(t)f\_{β^0}(Z)$, with $θ^0=(β^0,γ^0)^\top\in \mathbb{R}^{m+p}$. The baseline hazard function $η\_{γ^0}$ and relative risk $f\_{β^0}$ 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 $θ^0$ 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 $\sqrt{n}$-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 $\sqrt{n}$-consistent and asymptotically Gaussian in the Cox model and in the excess risk model, whatever is $f\_ε$.
dc.identifierhttps://arxiv.org/abs/math/0606192
dc.identifierhttp://arxiv.org/abs/math/0606192
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/131084
dc.subjectStatistics Theory
dc.subject62G05, 62F12, 62N01, 62N02; 62J02
dc.titleSemi-parametric estimation of the hazard function in a model with covariate measurement error
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