Weighted empiricals and the product-limit estimator in the multiplicative hazard and time transfer regression model

Abstract

In a model that combines the usual multiplicative hazard regression model and the accelerated life model or its log transform, weighted empirical processes are used to define estimators of the underlying hazard and survival functions with a specified multiplicative factor in the hazard rate. The covariates as well as the weights are allowed to be time-dependent. The weak convergence of the estimators are obtained. These estimators can be used to define and analyze parametric estimators in the multiplicative hazard model, the censored regression or the accelerated life model.