BOUNDARY AWARE ESTIMATORS OF INTEGRATED DENSITY DERIVATIVE PRODUCTS

Integrated squared density derivatives are important to the plug-in ty pe of bandwidth selector for kernel density estimation. Conventional e stimators of these quantities are inefficient when there is a non-smoo th boundary in the support of the density. We introduce estimators tha t utilize density derivative estimators obtained from local polynomial fitting. They retain the rates of convergence in mean-squared error t hat are familiar from non-boundary cases, and the constant coefficient s have similar forms. The estimators and the formula for their asympto tically optimal bandwidths, which depend on integrated products of den sity derivatives, are applied to automatic bandwidth selection for loc al linear density estimation. Simulation studies show that the constru cted bandwidth rule and the Sheather-Jones bandwidth are competitive i n non-boundary cases, but the former overcomes boundary problems where as the latter does not.