  We study schemes and lower bounds for distributed minimax statistical
estimation over a Gaussian multiple-access channel (MAC) under squared error
loss, in a framework combining statistical estimation and wireless
communication. First, we develop "analog" joint estimation-communication
schemes that exploit the superposition property of the Gaussian MAC and we
characterize their risk in terms of the number of nodes and dimension of the
parameter space. Then, we derive information-theoretic lower bounds on the
minimax risk of any estimation scheme restricted to communicate the samples
over a given number of uses of the channel and show that the risk achieved by
our proposed schemes is within a logarithmic factor of these lower bounds. We
compare both achievability and lower bound results to previous "digital" lower
bounds, where nodes transmit errorless bits at the Shannon capacity of the MAC,
showing that estimation schemes that leverage the physical layer offer a
drastic reduction in estimation error over digital schemes relying on a
physical-layer abstraction.
