Nonparametric inference for the proportionality function in the random censorship model

By generalizing the proportional hazards model, we introduce a new function beta(t), which we call the proportionality function, and which we show plays a role in studying aspects of the randomly censored model. We develop an asymptotically efficient nonparametric estimator of beta(t), establish its uniform consistency, and obtain a weak convergence result. Furthermore, a confidence band for beta(t), based on the bootstrap, is developed. The results are applied to an actual dataset.