795

NONPARAMETRIC CONFIDENCE SETS FOR DENSITIES

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.





Keywords: Confidence Sets, nonparametric density estimation, shrinkage methods, empirical processes.



Heidi Sestrich 2004-03-02
Here is the full PDF text for this technical report. It is 1183353 bytes long.