Conditional hazard rate estimation for right censored data

Abstract

Theory and methodology of nonparametric sharp minimax estimation of the conditional hazard rate function of a right censored lifetime given a continuous covariate are developed. The theory, using an oracle’s approach, shows how the conditional hazard and nuisance functions affect rate and constant of the mean integrated squared error (MISE) convergence. The methodology suggests a data-driven estimator matching performance of the oracle. Further, if the lifetime is independent of the covariate, the estimator recognizes that and the MISE converges with the univariate rate. Then the setting is extended to a vector of continuous and ordinal/nominal categorical predictors, and an estimator performing adaptation to smoothness and dimensionality of conditional hazard is suggested. Practical examples devoted to reducing potent greenhouse gas emissions are presented.