Asymptotic expansion for ISE of kernel density estimators under censored dependent model

In some long term studies, we encounter a series of dependent and censored observations. Randomly censored data consist of i.i.d. pairs of observations (Xi,δi)i=1,…,n(Xi,δi)i=1,…,n. If δi=0δi=0, XiXi denotes a censored observation, and if δi=1δi=1, XiXi denotes a survival time, which is the variable of interest. One of the global stochastic measures of the distance between a density and its kernel density estimator is integrated square error. In this paper, we apply the technique of strong approximation to establish an asymptotic expansion for the integrated square error of the kernel density estimate, when censored data are showing some kind of dependence.