In search of an optimal kernel for a bias correction method for density estimators

We consider a bias correction method for kernel density estimators based on a generalized jack-knifing with different bandwidths. We compare it with a standard kernel density estimation method with fourth order kernels, since both methods have the same rate of convergence. The bias corrected method has a tuning parameter. We investigate how to optimize the constant in the asymptotical mean integrated squared error of the bias corrected estimator with respect to the tuning parameter. We also explore whether an optimal kernel exists. This paper answers on the questions posed in section 3.2 of Jones and Foster (1993) where only numerical investigation was given.