  Under Markovian assumptions, we leverage a Central Limit Theorem (CLT) for
the empirical measure in the test statistic of the composite hypothesis
Hoeffding test so as to establish weak convergence results for the test
statistic, and, thereby, derive a new estimator for the threshold needed by the
test. We first show the advantages of our estimator over an existing estimator
by conducting extensive numerical experiments. We find that our estimator
controls better for false alarms while maintaining satisfactory detection
probabilities. We then apply the Hoeffding test with our threshold estimator to
detecting anomalies in two distinct applications domains: one in communication
networks and the other in transportation networks. The former application seeks
to enhance cyber security and the latter aims at building smarter
transportation systems in cities.
