An Estimator of Monotone Regression Function With Randomly Right Censored Data

The aim is to gain a rational estimator of monotone regression function with randomly right censored data.Using the theory of the greatest convex minorant and the statistical idea of padding the uncensored data highly, a new estimator is proposed.The estimator can guarantee monotone property, which is superior to traditional kernel estimators.Thus, in practical applications, such as establishing children's growth curve, when right censored data comes up and the regression function can be concluded to be monotone by historical experience or common sense, this estimation method is more natural.Under assumed conditions, the asymptotic distribution of the estimator is found and the estimator is shown to be consistent, indicating that the estimator has good limit behaviors.