Multistage plug-in bandwidth selection for kernel distribution function estimates
The use of a kernel estimator as a smooth estimator for a distribution function has been suggested by many authors. An expression for the bandwidth that minimizes the mean integrated square error asymptotically has been available for some time. However, few practical data based methods for estimating this bandwidth have been investigated. In this paper we propose a multistage plug-in type estimator for this optimal bandwidth, and derive its asymptotic properties. In particular we show that two stages are required for good asymptotic properties. This behavior is verified for finite samples using a simulation study.
smoothing plug-in rule normal reference rule oversmoothing bandwidth squared error loss survival function