  The paper studies the problem of distributed parameter estimation in
multi-agent networks with exponential family observation statistics. A
certainty-equivalence type distributed estimator of the consensus + innovations
form is proposed in which, at each each observation sampling epoch agents
update their local parameter estimates by appropriately combining the data
received from their neighbors and the locally sensed new information
(innovation). Under global observability of the networked sensing model, i.e.,
the ability to distinguish between different instances of the parameter value
based on the joint observation statistics, and mean connectivity of the
inter-agent communication network, the proposed estimator is shown to yield
consistent parameter estimates at each network agent. Further, it is shown that
the distributed estimator is asymptotically efficient, in that, the asymptotic
covariances of the agent estimates coincide with that of the optimal
centralized estimator, i.e., the inverse of the centralized Fisher information
rate. From a technical viewpoint, the proposed distributed estimator leads to
non-Markovian mixed timescale stochastic recursions and the analytical methods
developed in the paper contribute to the general theory of distributed
stochastic approximation.
