Theoretical and computational issues related to optimal bandwidth selection for nonparametric quantile estimation DANA FLOREA-DRAGHICESCU University of Chicago Center for Integrating Statistical and Environmental Science  We investigate the problem of optimal bandwidth selection for kernel estimators of probability distribution functions leading to quantile estimators for time-dependent transformations of stationary Gaussian processes with short and long memory.  We prove theoretical properties of the time-dependent optimal bandwidths obtained by minimizing the integrated mean squared error of the aforementioned kernel estimators.  A simulation study and a practical application are included to illustrate the findings.