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

We consider a model where the failure hazard function, conditional on a covariate $Z$ is given by $R(t,\theta^0|Z)=\eta\_{\gamma^0}(t)f\_{\beta^0}(Z)$, with $\theta^0=(\beta^0,\gamma^0)^\top\in \mathbb{R}^{m+p}$. The baseline hazard function $\eta\_{\gamma^0}$ and relative risk $f\_{\beta^0}$ belong both to parametric families. The covariate $Z$ is measured through the error model $U=Z+\epsilon$ where $\epsilon$ is independent from $Z$, with known density $f\_\epsilon$. 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 $\theta^0$ 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 $f\_\epsilon$ and $f\_\beta(z)$ 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 $f\_\epsilon$

Individual and Collective Resources and Health in Morocco

The interaction between available individual and collective resources in the determination of health is largely ignored in the literature on the relationship between poverty and health in developing countries. We analyse the role public resources play in the perception that rural women in Morocco have of their health. These resources are taken to contribute directly and indirectly to the improvement of individual health by, on the one hand, providing a health-promoting environment and, on the other, improving the individual?s ability to produce health. The empirical results of multilevel models confirm the expected associations between socioeconomic status, individual vulnerability factors and health. Furthermore, the random part of the model suggests that variation in state of health is also associated with the presence of collective resources. However, the higher the level of women?s individual wealth, the less the characteristics of the community in which they live seem to be associated with their health, and the less the potential vulnerability factors seem to constrain their ability to maintain or improve health. Our results suggest that collective investments derived from various areas of activity will be more favourable to improving health, insofar as they are adapted to the initial capacity of women to benefit from them.health, poverty, rural, women, Morocco

On a Boltzmann mean field model for knowledge growth

In this paper we analyze a Boltzmann type mean field game model for knowledge growth, which was proposed by Lucas and Moll. We discuss the underlying mathematical model, which consists of a coupled system of a Boltzmann type equation for the agent density and a Hamilton-Jacobi-Bellman equation for the optimal strategy. We study the analytic features of each equation separately and show local in time existence and uniqueness for the fully coupled system. Furthermore we focus on the construction and existence of special solutions, which relate to exponential growth in time - so called balanced growth path solutions. Finally we illustrate the behavior of solutions for the full system and the balanced growth path equations with numerical simulations.Comment: 6 figure