Asymptotic Properties Of Plug-in Level Set Estimator For Right Censored Data

We assume T1,...,Tnare i.i.d.random samples from distribution function F withdensity function f and C1,...,Cnare i.i.d.random samples from distribution functionG.Observed data consists of pairs (Xi, δi), i=1,..., n, where Xi=min{Ti,Ci},δi=I(Ti≤Ci), I(A) denotes the indicator function of set A.Based on the right cen-sored data {Xi, δi},i=1,..., n, we consider the problem of estimating the level set{f≥c} of an unknown one-dimensional density function f and study the asymptoticbehavior of the plug-in level set estimator.Under some regularity conditions, we estab-lish the asymptotic normality and the exact convergence rate of theλg-measure of thesymmetric diference between the level set {f≥c} and its plug-in estimator {fn≥c},where f is the density function of F, and fnis a kernel-type density estimator of f.Simulation studies demonstrate that the proposed method is feasible.Illustration witha real data example is also provided.