Preadjusted non-parametric estimation of a conditional distribution function

Summary: The paper deals with non-parametric estimation of a conditional distribution function. We suggest a method of preadjusting the original observations non-parametrically through location and scale, to reduce the bias of the estimator. We derive the asymptotic properties of the estimator proposed. A simulation study investigating the finite sample performances of the estimators discussed is provided and reveals the gain that can be achieved. It is also shown how the idea of the preadjusting opens the path to improved estimators in other settings such as conditional quantile and density estimation, and conditional survival function estimation in the case of censored data. © 2013 Royal Statistical Society.