Optimal Asymmetric Kernels

Abstract

Kernels are typically justified as a smoothing device in nonparametric analysis. We provide alternative interpretations which could lead to the use of asymmetric kernels. We thus derive the class of optimal asymmetric kernels, and analyse its main properties. We illustrate numerically its optimality by showing how well it fares in locating the mode and tail quantiles of some common asymmetric densities.