A Bridge from the Nearest Neighbour to the Fixed Bandwidth in Nonparametric Functional Estimation

Nonparametric functional estimation using kernel estimators is an evolving area of research in applied statistics with a direct connection to biometrical applications. For example, estimation of the hazard rate quantifies the instantaneous risk of failure or death that can be used in the context of medical survival analysis. We will deal with the crucial problem in practice, the bandwidth selection. A generalized bandwidth parameter incorporates as special cases the nearest neighbour and the fixed bandwidth. Implementation of this parameter in a kernel estimator points to solutions of the bandwidth selection problem. Consistency and rate of convergence of this generalized estimator are shown and support its use in practice.