  Markov chain Monte Carlo samplers produce dependent streams of variates drawn
from the limiting distribution of the Markov chain. With this as motivation, we
introduce novel univariate kernel density estimators which are appropriate for
the stationary sequences of dependent variates. We modify the asymptotic mean
integrated squared error criterion to account for dependence and find that the
modified criterion suggests data-driven adjustments to standard bandwidth
selection methods. Simulation studies show that our proposed methods find
bandwidths close to the optimal value while standard methods lead to smaller
bandwidths and hence to undersmoothed density estimates. Empirically, the
proposed methods have considerably smaller integrated mean squared error than
do standard methods.
