Behaviour of kernel density estimates and bandwidth selectors for contaminated data sets

In this paper robustness properties are studied for kernel density estimators. The plug in and the least squares cross validation bandwidth selectors are considered. In an asymptotic analysis and in a simulation study the performance of kernel density estimates is studied for contaminated data. It is shown that the robustness of kernel density estimates depends strongly on the chosen bandwidth selector. The plug in method is more appropriate when the statistical aim is estimation of the uncontaminated density, whereas the cross validation performs better in estimating the contaminated density. However, a simulation study suggests that, when using the cross validation, the gains in estimating the contaminated density are small compared to the losses in estimating the uncontaminated density.