Parametrically Assisted Nonparametric Estimation of a Density in the Deconvolution Problem
Aurore Delaigle, Peter Hall
Journal of the American Statistical Association | AMER STATISTICAL ASSOC | Published : 2014
Nonparametric estimation of a density from contaminated data is a difficult problem, for which convergence rates are notoriously slow. We introduce parametrically assisted nonparametric estimators which can dramatically improve on the performance of standard nonparametric estimators when the assumed model is close to the true density, without degrading much the quality of purely nonparametric estimators in other cases. We establish optimal convergence rates for our problem and discuss estimators that attain these rates. The very good numerical properties of the methods are illustrated via a simulation study. Supplementary materials for this article are available online.
We thank Dr. Mihee Lee for her help with early versions of codes and for useful discussion. We also thank the Australian Research Council for grant support, and the Institute for Mathematical Sciences of the National University of Singapore for their support.