Non-linear wavelet-based density estimators under random censorship

We provide an asymptotic expansion for the mean integrated squared error (MISE) of non-linear wavelet-based density estimators with randomly censored data. Our technique is facilitated by a result of Stute (Ann. Statist. 23 (1995) 422) that approximates the Kaplan-Meier integrals by an average of i.i.d. random variables with a certain rate. We show this MISE expansion, when the underlying survival density function and censoring distribution function are only piecewise smooth, is the same as analogous expansion for the kernel density estimators. However, for the kernel estimators, this MISE expansion holds only under the additional smoothness assumption. (C) 2002 Elsevier B.V. All rights reserved.