Adaptive estimation of the hazard rate with multiplicative censoring

Abstract

We propose an adaptive estimation procedure of the hazard rate of a random variable X in the multiplicative censoring model, Y=XU, with U∼U([0,1]) independent of X. The variable X is not directly observed: an estimator is built from a sample {Y1,...,Yn} of copies of Y. It is obtained by minimisation of a contrast function over a class of general nested function spaces which can be generated e.g. by splines functions. The dimension of the space is selected by a penalised contrast criterion. The final estimator is proved to achieve the best bias–variance compromise and to reach the same convergence rate as the oracle estimator under conditions on the maximal dimension. The good behavior of the resulting estimator is illustrated over a simulation study.