Tilted and Data-Sharpened Nonparametric Density Estimation

High-order nonparametric density estimators built by perturbing a conventional kernel estimator, either by re-weighting the observations ("tilting") or by moving them ("data sharpening"). The perturbation is chosen so that the estimator inherits the fast convergence rate of an infinite-order kernel estimator, such as the sinc or trapezoidal flat-top estimator, while remaining a proper non-negative density without the oscillatory tails those estimators suffer from. Two criteria are provided: minimising the L2 distance to an infinite-order comparator, following Doosti and Hall (2016) , and minimising a cross-validation criterion that needs no comparator and is much faster, following Doosti, Hall and Mateu (2018) .