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We consider the problem of distributed estimation, where local processorsobserve independent samples conditioned on a common random parameter ofinterest, map the observations to a finite number of bits, and send these bitsto a remote estimator over independent noisy channels. We derive converseresults for this problem, such as lower bounds on Bayes risk. The maintechnical tools include a lower bound on the Bayes risk via mutual informationand small ball probability, as well as strong data processing inequalities forthe relative entropy. Our results can recover and improve some existing resultson distributed estimation with noiseless channels, and also capture the effectof noisy channels on the estimation performance.

Converses for distributed estimation via strong data processing inequalities