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Rychlik, Tomasz
Year of Publication: 
Series/Report no.: 
SFB 373 Discussion Paper 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
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Working Paper

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