A General Kernel Functional Estimator with Generalized Bandwidth - Strong Consistency and Applications

Abstract

We consider the problem of uniform asymptotics in kernel functional estimation where the bandwidth can depend on the data. In a unified approach we investigate kernel estimates of the density and the hazard rate for uncensored and right-censored observations. The model allows for the fixed bandwidth as well as for various variable bandwidths, e.g. the nearest neighbor bandwidth. An elementary proof for the strong consistency of the generalized estimator is given that builds on the local convergence of the empirical process against the cumulative distribution function and the Nelson-Aalen estimator against the cumulative hazard rate, respectively.