Estimation in Linear-Rate Simple Survival Models with Measurement Errors and Censoring

A simple exponential regression model is considered where the rate parameter of the response variable linearly depends on the explanatory variable. We consider complications of the model: censoring of the response variable (either upper censoring or interval observations), the additive classical error or multiplicative Berkson error in the explanatory variable, or a combination of censoring with Berkson errors. We construct or use already-known estimators in the models, and verify their performance in simulations.