Nonparametric regression with filtered data

We present a general principle for estimating a regression function nonparametrically allowing for a wide variety of data Öltering, e.g., repeated left truncation and right censoring. Both the mean and the median regression case are considered. The method works by Örst estimating the conditional hazard function or conditional survivor function and then integrating. We also investigate improved methods that take account of model structure such as independent errors, and show that such methods can improve performance when the model structure is true. We establish the pointwise asymptotic normality of our estimators.