Smoothed stationary bootstrap bandwidth selection for density estimation with dependent data

A smoothed version of the stationary bootstrap is established for the purpose of bandwidth selection in density estimation for dependent data. An exact expression for the bootstrap version of the mean integrated squared error under dependence is obtained in this context. This is very useful since implementation of the bootstrap selector does not require Monte Carlo approximation. A simulation study is carried out to show the good practical performance of the new bootstrap bandwidth selector with respect to other existing competitors. The method is illustrated by applying it to two real data sets.