Miscellanea. Data sharpening as a prelude to density estimation

Abstract

We introduce a data-perturbation method for reducing bias of a wide variety of density estimators, in univariate, multivariate, spatial and spherical data settings. The method involves 'sharpening' the data by making them slightly more clustered than before, and then computing the estimator in the usual way, but from the sharpened data rather than the original data. The transformation depends in a simple, explicit way on the smoothing parameter employed for the density estimator, which may be based on classical kernel methods, orthogonal series, histosplines, singular integrals or other linear or approximately-linear methods. Bias is reduced by an order of magnitude, at the expense of a constant-factor increase in variance.