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Statistics Seminar Series

Thursday, November 29, 2007 @ 4:00PM
Fenster Hall Room 425
New Jersey Institute of Technology

Boundary Correction Methods in Kernel Density Estimation

Tom Alberts

Courant Institute of Mathematical Sciences,

New York University

The term density estimation refers to the broad methodology used in constructing estimators of an unknown probability density function given an i.i.d. sample of data from the density. Non-parametric kernel density estimation is a commonly used and attractive method, due to its ease of implementation and good statistical properties such as low bias and variance. For densities with support on an interval the standard kernel density estimator suffers from boundary effects near the endpoints, and in fact is not even consistent (although it still has low variance).

In this talk I describe the basic construction of a kernel density estimator and propose a simple yet effective modification that restores the consistency in the boundary region, while at the same time maintaining the low variance. This is joint work with my former research supervisor, R.J. Karunamuni.