A note on kernel polygons

Jones (1989) has pointed out that piecewise linear interpolated kernel density estimators on a sufficiently fine grid can be visually indistinguishable from the true density. A simple device, the kernel polygon, is proposed for eliminating the evaluation of the normalisation constant of the estimator while retaining its property of being a density function as well as providing practical advantages. The class of uniform and linear kernels of the kernel polygons is given. Finally, we present a simulation study and a real data example in which we compare bandwidth selectors for the kernel polygons. Copyright 2006, Oxford University Press.