Department of Statistics Unitmark
Dietrich College of Humanities and Social Sciences

NONPARAMETRIC CONFIDENCE SETS FOR DENSITIES

Publication Date

March, 2004

Publication Type

Tech Report

Author(s)

Woncheol Jang, Christopher Genovese, and Larry Wasserman

Abstract

We present a method for constructing nonparametric confidence sets for density functions based on an approach due to Beran and Dümbgen (1998). We expand the density in an appropriate basis and we estimate the basis coefficients by using linear shrinkage methods. We then find the limiting distribution of an asymptotic pivot based on the quadratic loss function. Inverting this pivot yields a confidence ball for the density.

(Revised 10/04)

Areas of Research