Estimator of the Optimal Bandwidth
We propose an estimator
of the optimal bandwidth to be used in the definition of the kernel estimator
of the distribution function. By using characteristic function and results
from the analysis, we prove that this estimator is strongly consistent in the
i.i.d. case. By using the results of this work we improve the Tajima's test.
Tajima's test is based on the assumption that the statistic defined in the
test follows a beta distribution, but from some simulations results it was
found that this assumption in some cases is no correct. In those cases we
define the critical region by using kernel estimator.