Conditional mean residual life estimation

Abstract

In this paper, we consider the problem of nonparametric mean residual life (MRL) function estimation in presence of covariates. We propose a contrast that provides estimators of the bivariate conditional MRL function, when minimised over different collections of linear finite-dimensional function spaces. Then we describe a model selection device to select the best estimator among the collection, in the mean integrated squared error sense. A non-asymptotic oracle inequality is proved for the estimator, which both ensures the good finite sample performances of the estimator and allows us to compute asymptotic rates of convergence. Lastly, examples and simulation experiments illustrate the method, together with a short real data study.