Spline regression for hazard rate estimation when data are censored and measured with error

In this paper, we study an estimation problem where the variables of interest are subject to both right censoring and measurement error. In this context, we propose a nonparametric estimation strategy of the hazard rate, based on a regression contrast minimized in a finite-dimensional functional space generated by splines bases. We prove a risk bound of the estimator in terms of integrated mean square error and discuss the rate of convergence when the dimension of the projection space is adequately chosen. Then we define a data-driven criterion of model selection and prove that the resulting estimator performs an adequate compromise. The method is illustrated via simulation experiments that show that the strategy is successful.