  The identification of anomalies is a critical component of operating complex,
and possibly large-scale and geo-graphically distributed cyber-physical
systems. While designing anomaly detectors, it is common to assume Gaussian
noise models to maintain tractability; however, this assumption can lead to the
actual false alarm rate being significantly higher than expected. Here we
design a distributionally robust threshold of detection using finite and fixed
higher-order moments of the detection measure data such that it guarantees the
actual false alarm rate to be upper bounded by the desired one. Further, we
bound the states reachable through the action of a stealthy attack and identify
the trade-off between this impact of attacks that cannot be detected and the
worst-case false alarm rate. Through numerical experiments, we illustrate how
knowledge of higher-order moments results in a tightened threshold, thereby
restricting an attacker's potential impact.
