NONPARAMETRIC CONFIDENCE SETS FOR DENSITIES
Woncheol Jang, Christopher Genovese, and Larry Wasserman
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.