BEHAVIOR OF KERNEL DENSITY ESTIMATES AND BANDWIDTH SELECTORS FOR CONTAMINATED DATA SETS

In this paper robustness properties are studied for kernel density est imators. The plug in and the least squares cross validation bandwidth selectors are considered. In an asymptotic analysis and in a simulatio n study the performance of kernel density estimates is studied for con taminated data. It is shown that the robustness of kernel density esti mates depends strongly on the chosen bandwidth selector. The plug in m ethod is more appropriate when the statistical aim is estimation of th e uncontaminated density, whereas the cross validation performs better in estimating the contaminated density. However, a simulation study s uggests that, when using the cross validation, the gains in estimating the contaminated density are small compared to the losses in estimati ng the uncontaminated density.