  Density estimation is a classical problem in statistics and has received
considerable attention when both the data has been fully observed and in the
case of partially observed (censored) samples. In survival analysis or clinical
trials, a typical problem encountered in the data collection stage is that the
samples may be censored from the right. The variable of interest could be
observed partially due to the presence of a set of events that occur at random
and potentially censor the data. Consequently, developing a methodology that
enables robust estimation of the lifetimes in such setting is of high interest
for researchers.
  In this paper, we propose a non-parametric linear density estimator using
empirical wavelet coefficients that are fully data driven. We derive an
asymptotically unbiased estimator constructed from the complete sample based on
an inductive bias correction procedure. Also, we provide upper bounds for the
bias and analyze the large sample behavior of the expected $\mathbb{L}_{2}$
estimation error based on the approach used by Stute (1995), showing that the
estimates are asymptotically normal and possess global mean square consistency.
  In addition, we evaluate the proposed approach via a theoretical simulation
study using different exemplary baseline distributions with different sample
sizes. In this study, we choose a censoring scheme that produces a censoring
proportion of 40\% on average. Finally, we apply the proposed estimator to real
data-sets previously published, showing that the proposed wavelet estimator
provides a robust and useful tool for the non-parametric estimation of the
survival time density function.
