Asymptotically Optimal Bandwidth Selection for Kernel Density Estimators from Randomly Right-Censored Samples

Abstract

This paper makes two important contributions to the theory of bandwidth selection for kernel density estimators under right censorship. First, an asymptotic representation of the integrated squared error into easily understood variance and squared bias components is given. Second, it is shown that if the bandwidth is chosen by the data-based method of least-squares cross-validation, then it is asymptotically optimal in a compelling sense. A by-product of the first part is an interesting comparison of the two most popular kernel estimators.