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Statistics Seminar Series


Wednesday, April 18, 2007 @ 4:00PM
Cullimore Hall, Room 611
New Jersey Institute of Technology

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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.