The bootstrap in nonparametric density estimation

Let X(1),X(2),...,X(n) an i.i.d. random variables with unknown density f. And let Y-1(b),...,Y-n(b), a bootstrap sample of size n drawn as Taylor's [11] from the sample X(1),...,X(n). We bootstrap the Parzen-Rosenblatt's ([9], [10]) density estimate f(n,h). and study the optimal bandwith, which minimizes the bootstrapped MISE. Then we give the variance of the bootstrapped ISE.