Relative efficiency of local bandwidths in kernel density estimation

The concept of relative efficiency can be used in kernel density estimation to analyze the global benefits of the optimal local bandwidth selector wit h respect to the optimal global one, in terms of MISE. This index, as well as its asymptotic counterpart -the asymptotic relative efficiency-, can be used to regard if the use of a local selector is worthwhile. This, of cours e, depends on the underlying density. Some bootstrap estimator of the relat ive efficiency index is presented in this paper and proved to be consistent at the rate n(-1/7). The theory is illustrated with the computation of the relative efficiency of local bandwidths for a set of common densities and some simulations that show the good performance of its bootstrap estimator.