Authors

• V. Fakoor
• S. Jomhoori
• A. Ganjeali

Abstract

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.

Keywords

• Bandwidth
• integrated square error
• Kaplan-Meier estimator
• kernel density estimator
• strong mixing
• truncated dependent data