Minimum distance estimation of the center of symmetry with randomly censored data

A semi-parametric version of the Cramér-von Mises minimum distance estimator of the center of symmetry is considered when the data are subject to random censoring and the underlying distributions are unknown. The estimator is shown to be asymptotically normal. The proof uses the structural similarity with that in Koul and deWit, the convergence results for the Kaplan-Meier process in Gill and the mean square increment inequality for the Kaplan-Meier process in Yang. Some examples are given that extend some well known estimators in the complete data case.