Nonparametric density estimation over its unknown support for right censored data

The long-standing problem of nonparametric density estimation of the lifetime of interest over its unknown support, when only right-censored observations are available, is considered. Two cases, when the support of the lifetime of interest is a proper subset of the support of censoring variable and when the supports are the same, are explored. An orthogonal series density estimation, over a random interval defined by a specially chosen sequence of order statistics, is proposed and rates of the mean integrated squared error convergence are evaluated.