Discussion Papers, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 1999,6
For the problems of nonparametric estimation of nonincreasing and symmetric unimodal density functions with bounded supports we determine the projections of estimates onto the convex families of possible parent densities with respect to the weighted integrated squared error. We also describe the method of approximating the analogous projections onto the respective density classes satisfying some general moment conditions. The method of projections reduces the estimation errors for all possible values of observations of a given finite sample size in a uniformly optimal way and provides estimates sharing the properties of the parent densities.
error reduction Nonparametric density estimation monotone density symmetric unimodal density weighted integrated squared error projection