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Error reduction in density estimation under shape restrictions
Author(s) -
Rychlik Tomasz
Publication year - 1999
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3316116
Subject(s) - mathematics , bounded function , density estimation , regular polygon , estimation , reduction (mathematics) , sample (material) , nonparametric statistics , moment (physics) , statistics , mathematical optimization , mathematical analysis , geometry , estimator , chromatography , classical mechanics , economics , chemistry , management , physics
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.