Density Estimators for Truncated Dependent Data

In some long term studies, a series of dependent and possibly truncated lifetime data may be observed. suppose that the lifetimes have a common continuous distribution function f. a popular stochastic measure of the distance between the density function f of the lifetimes and its kernel estimate fn is the integrated square error (ise). in this paper, we derive a central limit theorem for the integrated square error of the kernel density estimators in the left-truncation model. it is assumed that the lifetime observations form a stationary strong mixing sequence. a central limit theorem (clt) for the ise of the kernel hazard rate estimators is also presented.