Some Asymptotic Properties of Kernel Density Estimation Under Length-Biased and Right-Censored Data

Among the various methods of density estimation, kernel smoothing is particularly appealing for both its simplicity and its interpretability. The main goal of this article is to study the large-sample properties of the kernel density estimator in the setting of length-biased and right-censored data. The almost sure representation of the distribution function estimator will be the key to obtaining the asymptotic representation for the kernel density estimator. This representation enables us to establish the asymptotic normality and uniform consistency of the estimator. A small simulation study is conducted to show how the estimator behaves for finite samples, and an application is also presented using real data.