Making a non-parametric density estimator more attractive, and more accurate, by data perturbation

Abstract

Motivated by both the shortcomings of high order density estimators, and the increasingly large data sets in many areas of modern science, we introduce new high order, non-parametric density estimators that are guaranteed to be positive and do not have highly oscillatory tails. Our approach is based on data perturbation, e.g. by tilting or data sharpening. It leads to new estimators that are more accurate than conventional kernel techniques that use positive kernels, but which nevertheless enjoy the positivity property, and are far less ‘wiggly’ than high order kernel estimators. We investigate performance by theoretical analysis and in a numerical study.