On the effect of misspecifying the error density in a deconvolution problem

The author studies the effect of a misspecification of the error density on the mean integrated squared error (MISE) of the deconvolution estimator. He shows that the MISE converges to a certain functional which he defines. He also illustrates the fact that the limit can sometimes be infinite. Finally, he derives some guidelines for selecting the error density in order to ensure robustness properties of the procedure.