Kernel estimation of a density based on contaminated data is considered and the important issue of how to choose the bandwidth parameter in practice is discussed. Some plug-in (PI) type of bandwidth selectors, which are based on non-parametric estimation of an approximation of the mean integrated squared error, are proposed. The selectors are a refinement of the simple normal reference bandwidth selector, which is obtained by parametrically estimating the approximated mean integrated squared error by referring to a normal density. A simulation study compares these PI bandwidth selectors with a bootstrap (BT) and a cross-validated (CV) bandwidth selector. It is concluded that in finite samples, an appropriately chosen PI bandwidth selector and the BT bandwidth selector perform comparably and both outperform the CV bandwidth. The use of the various practical bandwidth selectors is illustrated on a real data example.
['Aurore Delaigle', 'Irène Gijbels']
Practical bandwidth selection in deconvolution kernel density estimation