  We consider nonparametric estimation of cure-rate based on mixture model
under Case-1 interval censoring. We show that the nonparametric
maximum-likelihood estimator (NPMLE) of cure-rate is non-unique as well as
inconsistent, and propose two estimators based on the NPMLE of the distribution
function under this censoring model. We present a cross-validation method for
choosing a `cut-off' point needed for the estimators. The limiting
distributions of the latter are obtained using extreme-value theory. Graphical
illustration of the procedures based on simulated data are provided.
