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Statistics Seminar Series
Wednesday, April 18, 2007 @ 4:00PM
Cullimore Hall, Room 611
New Jersey Institute of Technology
Rank Adapted Kernel Density Estimation
David Kim, Ph.D
Department of Mathematics and Computer Science
Manhattan College
Riverdale, NY
Abstract
We consider adapting bandwidths of a kernel density estimator according to the ranks of observations. The specifics of bandwidth selection is motivated by a deterministic decomposition of a density into densities of order statistics and their asymptotic behaviors. The resulting estimator has a local bandwidth similar to that of Abramson (1982) and Breiman et al. (1977) with a new feature of rank correction. We investigate its properties and demonstrate that not only it can smooth out the bumps in the tails while maintaining interesting features in data-rich region but also that it can reduce the boundary bias when the support of the target density is compact.