  A parameter estimation problem is considered, in which dispersed sensors
transmit to the statistician partial information regarding their observations.
The sensors observe the paths of continuous semimartingales, whose drifts are
linear with respect to a common parameter. A novel estimating scheme is
suggested, according to which each sensor transmits only one-bit messages at
stopping times of its local filtration. The proposed estimator is shown to be
consistent and, for a large class of processes, asymptotically optimal, in the
sense that its asymptotic distribution is the same as the exact distribution of
the optimal estimator that has full access to the sensor observations. These
properties are established under an asymptotically low rate of communication
between the sensors and the statistician. Thus, despite being asymptotically
efficient, the proposed estimator requires minimal transmission activity, which
is a desirable property in many applications. Finally, the case of discrete
sampling at the sensors is studied when their underlying processes are
independent Brownian motions.
